I think this race is mostly balanced, but I have a few suggestions. Let's take each trait in turn from your stat block.
Ability Score Improvement: +2 Wis, +1 Con, +1 Str, -1 Dex
+2 to Wis and +1 to Con and Str would be balanced without needing the -1 Dex to counter-balance it, if we compare with Half-Elves (PHB, p. 39), who get +2 to Cha and +1 to two other abilities (thanks to András for reminding me).
Most other races have +2 and +1 to something (with the exception of Mountain Dwarves), and Triton (from Volo's Guide to Monsters, see p. 117), who has +1 to three different stats, so it's worth bearing in mind that this does make the race a little stronger, but I don't think the rest of the race's traits would make this overpowered.
Speed: 25 feet
Ok, slower than most other medium races, but the same as most small races; namely, Gnomes, Halflings and Dwarves all use this speed, so this is already something that exists, although it does make the race slightly weaker, but not by much.
I'm ignoring Age and Height, although I hope 8 feet means "as big as a Medium creature can get" (like a Goliath) because there are currently no Large playable races; in fact, so far the designers seem to have gone out of their way to avoid Large races, such as the playable Centaur and Minotaur races in Guildmaster's Guide to Ravnica being Medium, despite their monster counterparts (i.e. from the Monster Manual) being Large.
Natural Armour: You have natural armour which is equal to 10 + your proficiency bonus + your Constitution modifier.
There are a few other races that have natural armour traits, namely the Lizardfolk (Volo's, p. 113) or Loxodon (GGtR, p. 18), but they do not include the proficiency bonus. The Warforged from Wayfinder's Guide to Eberron have AC calculations that do include proficiency, so there is a precedent for it, but this has been changed in Eberron: Rising from the Last War to not include proficiency bonus, implying that it wasn't balanced after all. It might be best to go with the Loxodon's calculation, which is a flat 12 + your Constitution modifier.
Accustomed to the Forest: You gain advantage on all nature, survival checks concerning things in the forest.
On reflection, this might be quite overpowered, certainly at lower levels; it's more typical to give proficiency in a skill or two instead of advantage with those skills, given that advantage is equivalent to +5 (proficiency at lower levels is only +2, +4 with double proficiency, so having advantage instead is a bit much).
Spellcasting: you are able to cast the following spells:
You learn the cantrip thorn whip.
At 3rd level, you may cast entangle once per day.
At 5th level, you may cast speak with plants once per day.
This seems fine, although I assume this is using Wisdom as the spellcasting modifier? It's best to state that. The only one that may be atypical is that you can cast a 3rd level spell, speak with plants, but it's not a combat spell, and it is something that a full-spellcaster (i.e. a druid) could cast at 5th level, so I don't think this will be a problem or needs to be changed. Triton have already set a precedent for that in VGtM (they can cast wall of water at 5th level, which is a 3rd level spell, but it's not that strong-a-spell). It is otherwise in line with other races with innate spellcasting such as Tieflings (PHB, p. 43) or Drow (PHB, p. 24).
Languages: You know Common, Sylvan, and one other language of your choice.
Three languages? Most races only learn two, although there are some exceptions, such as the half elf (PHB, p. 39); high elves (PHB, p. 24) also gain an extra language. Overall, I don't think there's anything that makes this race overpowered, so I don't see an extra language tipping the balance.
All in all, this has some balance issues, but I think can be easily balanced with my recommended suggestions such as to the Natural Armour and Accustomed to the Forest traits. That said, it is on the stronger side of balanced, so adding anything else would very likely overpower it.
Spell Mimic is too flexible
I would not say that:
This feat is basically a watered down version of the arcane tricksters 17th level Spell Thief ability.
Because in many ways the Spell Mimic feat is better than the Spell Thief feature:
- The Spell Mimic's trigger is less specific than the Spell Thief's.
- The Spell Mimic cannot fail, whereas the Spell Thief can (and does more often than not).
- The Spell Thief's ability to reproduce a spell is implicitly limited to 4th level spells slots, whereas the Spell Mimic can even work with 9th level spells.
- The Spell Mimic recovers on short rests while the Spell Thief does not.
I'll grant you that in some respects Spell Mimic in inferior to Spell Thief:
- Spell Thief preserves the memory of the new spell for much much longer than Spell Mimic.
- Spell Mimic is implicitly useless with spells that have a casting time greater than 1 minute, whereas Spell Thief is not.
- the Spell Mimic may not use their prefered spellcasting ability, whereas the Spell Thief always uses intelligence.
But Spell Mimic also lacks effects that make Spell Thief better against foes and inefficient with allies:
- Spell Thief negates the triggering spell, whereas Spell Mimic does not.
- The target of Spell Thief forgets the triggering spell whereas the target of Spell Mimic does not.
This means Spell Mimic is best suited to reliably double the efforts of your allies instead of "using an opponent's strength against them".
In practice, Spell Mimic gives a caster temporary access to the spells prepared by the rest of the party when they are most needed and effective. This flexibility combined with some teamwork makes Spell Mimic unbalanced.
Whenever the party really needs something (whether it be heals, buffs, control, or raw damage) as long as at least one other caster can provide it, the character with Spell Mimic can double their efforts by mimicking their most suitable spell. Whereas it is much rarer for an opponent to use a spell worth mimicking in any given circumstance.
Then there are also class-specific shenanigans, like:
- A Warlock can use buffs (especially ones with long duration) and heals they usually don't have access to before a short rest.
- A Sorcerer can make up for their notoriously small amount of spells known.
- A Wizard can create contingencies of mimicked spells.
- A multiclass of two casters can mimick spells of a higher level than they can learn.
- A Tempest Cleric can spam a couple max-damage chain lightning.
- Etc.
My bare minimum recommendation to balance Spell Mimic is to somehow discourage targeting allies and limit it to spells of 5th level or lower.
However, it may be easier to achieve a feat that uses an opponent's strength against them via modifying something less convoluted than Spell Thief. I would explore an effect similar to the Ring of Spell Turning with adjustments like removing the advantage on saves and limiting which spell levels can be turned to match the growth of a half-caster.
Best Answer
I am not sure that your research was very thorough, so I am going to challenge the frame of your question a little bit here. I also observe that you are overcomplicating the issue somewhat - but that's not uncommon. I tried a homebrew druid sub class a while back that, on first review here, was found to be overcomplicated.
There are features and feats that already boost healing.
If you want to boost your healing ability the simplest way is to
Play a life domain cleric
(Citations are from the Basic Rules, p. 25 (same as PHB section on Life Domain Cleric).
Disciple of Life
Channel Divinity: Preserve Life
Experience: My life clerics used this A Lot.
Blessed Healer
You need not expend many, or any, resources healing yourself if you are healing others a lot.
Supreme Healing (if your game gets that far)
When you upcast spells at a higher level, that's a huge boost to healing. Example: 4d6 averages 14, 4d6 with the above feaure is 24.
If you go variant Human for your player race, you can add a feat at level 1.
Two of them in the PHB boost healing quite a bit, although the second one relies on synergy with Life domain Cleric to really shine.
Healer Feat. This is extremely useful. Our Tempest Cleric in a Tier 3 campaign (we were at level 14) was still using the second feature on our party routinely.
That first feature is really nice for getting people up who are at 0 HP. The difference between 1 HP and 0 HP is mechanically significant. You can run, act, hide, whatever at 1 HP. At 0 HP, you are unconscious.
Magic Initiate: if you are playing the life domain cleric, take the Goodberry spell (it synergizes with disciple of Life, so you end up adding 3 points to each one point berry) and two other druid cantrips. (I took guidance and shillelagh). (PHB, Ch 6).
At table experience: this really boosts the pool of HP you can heal your party with between encounters, particularly at low levels. 40 HP per long rest restored, and, your party never needs food since goodberry feeds them.
Temporary Hit Points: an ounce of prevention is worth a lot.
Damage that you and your allies don't take does not need to be healed.
If playing a non-cleric, non-druid class (particularly if they have high charisma like a bard, sorcerer or paladin) the Inspiring Leader Feat offers your allies temporary hit points once per short rest: damage they don't take does not have to be healed.
If your bard with charisma 18 at level 4 applies this, the party each has 8 Temp HP. That's damage they don't take and thus don't need to heal during the next combat encounter.
A special shout out goes to the Artificer, Artillerist, who has a Protector option for their cannon that provides significant Temp HP as a bonus action each round. We have discovered in play that this is incredibly useful to the point of approaching overpowered. In one fight at 4th level, I tallied up all of the damage that temp HP had soaked up: it was over 100 HP for a five person party. (Me DM). Once again, damage you that don't take does not have to be healed.
One more spell that I will mention is Heroism. If you are playing a class that has access to this spell, it provides temporary hit points each round - and it refreshes each round. (Temp HP usually do not refresh). At low levels in particular, this prevents significant damage and precludes some of the need for healing
Caveat: the Temp HP go away after the spell ends. Normal Temporary Hit Points last until used up or a long rest is completed.
Play a Druid, Circle of the Shepherd
At 3rd level a very nice healing spell arrives (Healing Spirit), and, there's a spirit starting at second level that provides a temporary hit Points option. See above regarding temp HP. The druid also has access to normal healing spells.
The above is not an exhaustive list, just some of the ones I've seen in play that are very effective.
Bottom Line: you don't need this feat
There are already a number of features, and feats, that do what you want to do: boost healing, and/or prevent damage (which renders the need for healing moot). I suggest that you use them (being new players) and not overcomplicate the game with a feat that isn't built with a solid understanding of the game's balance point. (And this helps your DM out by not forcing them into a play test mode. Your question points out that this is a concern to your DM).
As an aside, I agree with SeriousBri's answer on this feat being out of balance/broken.
Make Use of Short Rest Organic Healing
Lastly: a lot of new players to this edition, and DMs, don't apply the use of Hit Die based healing very effectively.
Short Rest (Basic Rules, p. 70; PHB Chapter 8)
Taking short rests, and healing by rolling your hit dice makes for another healing resource that I have seen under used at most of the tables where I have played. When we started out, all of us having played previous editions, that mechanic was not well understood and barely used.
I can't emphasize this enough: as a party, and as a table, become very familiar with the use of HD to heal yourself (all PCs) during short rests. Apply it. Those HD are a healing resource. Use them.