This Dhampir race is effectively a weaker version of a Drow, so I'll compare it to that.
- Ability Score Increase: The Dhampir gets to choose between the ability score bonuses of the Drow and those of the Dragonborn. This is perfectly in line with existing races.
Stuff the Dhampir gets:
Age & Alignment: Don't really matter from a balance perspective.
Size: The same as everyone else.
Speed: The same as almost everyone else, including the Drow.
Superior Darkvision: The same as the Drow.
Sunlight Sensitivity: The same as the Drow.
Dhampir Magic: The Dhampir gets a 1st level spell 1/day at 1st level, and a 2nd level spell 1/day at 3rd level. The Drow gets a cantrip, a 1st level spell 1/day at 3rd level, and a 2nd level spell 1/day at 5th level. This is the first real difference between the two. The Dhampir gets their racial spells 2 levels earlier, which is obviously stronger up until 5th level when it stops mattering. Not getting a free cantrip goes a fair way towards balancing this out, though.
Vampiric Heritage: I'll come back to this.
- Vampire Weaknesses: If you're incapacitated in a place of rest, you're probably asleep. It's pretty easy to kill someone who's asleep in general, so this doesn't really change much. There might be niche cases where it really comes into play but most of the time it shouldn't matter much.
Languages: Common and one other, just like every other race. The freedom to choose is nice, but hardly imbalancing.
Stuff the Dhampir doesn't get that the Drow does:
- Keen Senses: Free proficiency in the most important skill in the game. This is pretty strong.
Fey Ancestry: Advantage on saving throws against some of the most dangerous spells in the game, and immunity to the Sleep spell. This is also pretty strong.
Trance: Depending on your group and your DM, this might be important, but for most players, it's not going to matter a whole lot.
Drow Weapon Training: This is kind of nice, but most builds that need weapon proficiencies involve a class that gives them, so it's not that nice.
Overall, the Dhampir is probably a weaker version of the Drow. Their racial magic trait is a little better before level 5, but after that it's the same, minus a cantrip. Now for the elephant in the room.
Vampiric Heritage
Whenever you grapple, incapacitate, or restrain a creature, you gain the ability to bite that creature dealing 1d6 piercing damage. Furthermore, you can spend your turn drinking the blood of that creature, causing it to loss [sic] 1d6 necrotic damage. The creature's hit point maximum is reduced by an amount equal to the necrotic damage taken, and you regains [sic] hit points equal to that amount. The reduction lasts until the creature finishes a long rest, it dies if this effect reduces its hit point maximum to 0.
The problem with this is "the ability to bite that creature dealing 1d6 piercing damage". Does this require an action? A bonus action? No action at all? Does it give you the ability to do that when you grapple them, or anytime while you're grappling them? It doesn't really give us anyway to know.
The good news is that it doesn't really matter. Unless it requires no action and is anytime while you're grappling them, this is a pretty weak ability. If it's free when you grapple them, you can grapple, bite, let go, grapple, bite, let go and so on up to 4 times (if you're a Fighter). Except that you're just dealing 1d6 damage, so you'd have been better off attacking normally. Assuming your Strength score is 16 or higher, you'd have been better off punching them!
It only gets worse with other interpretations, too. If it requires an action and you can do it anytime while grappling, you're effectively using a turn to deal 1d6 damage, which is pretty much a joke.
Moving along to the other half of the ability, we have the ability to spend your turn drinking the blood of a creature. It's pretty clear what "spend your turn" means, and it makes for a pretty useless ability. Using your entire turn to deal 1d6 damage and gain 1d6 hit points might be ok at level 1 but it's going to become a joke pretty quickly.
The reducing maximum hit points part is useless because if you do enough damage to kill them with it, they would have died anyway. In general, D&D characters want to kill things, not inconvenience them. It could be used as a way to prevent an enemy regaining hit points, but there's a cantrip that does the job better and more efficiently.
So, overall, the Dhampir is pretty much a weakened version of the Drow race with some unique but useless features.
Best Answer
The NPCs ability to grant inspiration every turn doesn't in any way alter inspirations normal limitations. Inspiration can potentially be used multiple times in a single turn (or on any other creature's turn), so granting a single use of it per NPC's turn in no way implies it should change its current limitations. Similarly, a generous DM could simply award inspiration every round for immersive descriptions of attacks or ability checks.
Consider for example Heroism.
It grants more temporary hit points every turn. However that in no way removes Temporary Hit Points built in limitation of not-stacking.