Yes.
In order to cast the spell, you must provide the following material component (from the spell description):
a quiver containing at least one piece of ammunition
If you have a quiver containing a silver arrow and an adamantine arrow, you fulfill the material component requirements of the spell. In other words, the quiver of at least one arrow (not simply an arrow by itself) is the material component.
Then, here's how the spell's effect works (from the description, emphasis mine):
You transmute your quiver so it produces an endless supply of nonmagical ammunition...
On each of your turns until the spell ends, you can use a bonus action to make two attacks with a weapon that uses ammunition from the quiver. Each time you make such a ranged attack, your quiver magically replaces the piece of ammunition you used with a similar piece of nonmagical ammunition...
Once the quiver is transmuted, each attack you make using ammunition from the quiver causes the quiver to automatically replace that ammunition with a similar sort. Since you make multiple attacks during the spell's duration, each attack with an original arrow produces a replacement arrow, which then gets used and replaced, which then gets used and replaced, and so on.
As you correctly noted, silver and adamantine ammunition are not inherently magical, so each replacement arrow will be of similar make. But, do note the following (from the description):
Any pieces of ammunition created by this spell disintegrate when the spell ends.
So once you've shot one of the original pieces of ammunition, no matter how many times you can continue to replace and shoot the replacement again for the duration of the spell, once the spell is over the original (which you've shot away) and any of its replacements (which disintegrate) will be gone. Thus if you start with only a silver arrow and an adamantine arrow and you fire both silver and adamantine arrows during the spell's duration, you'll be left with an empty quiver (unless you can recover the original arrows subject to the normal ammo recovery rules).
In addition to the other answers, I would say that from a role-playing perspective it makes sense that Heavy Armor Optimization fits. The description of the feat is
You have trained extensively in heavy armor, and you have learned to take advantage of the protection it offers.
To me this implies that your character has learned to use the extra protection of the armor to their advantage when fighting. Some examples of using this to your advantage might be
- Heavy gauntlets on your hands allow you to use your hands to deflect blows
- If a swing or thrust is directed to an especially resilient place (i.e. your chest) you know that it will deflect easily and won't need to brace yourself as much
- You can focus your dodging to moving your vulnerable spots away from the attack rather than moving your entire body.
Any of the above still applies to Mithral Heavy Armor. Even though it weighs less, you can still capitalize on the advantages you get by being more armored.
Best Answer
There are magic and non-magic items made from adamantine
While the DMG lists Adamantine Armor as a magic item, some items made from adamantine are not magic.
Gargoyles resist damage from “nonmagical weapons that aren’t adamantine” (MM, p 140). It follows there would be nonmagical weapons that are adamantine.
So, adamantine weapons would strike gargoyles similarly to how magic weapons would, without being magic weapons, or even magic items. Mechanically, they are similar to silvered weapons (the phrasing in monsters’ resistances blocks are the same) but they defeat a different set of monsters’ damage resistances.
Xanathar’s Guide does not call Adamantium “Magical”
Xanathar’s Guide to Everything (p. 78) has a section on adamantium weapons which describes adamatine as “an ultrahard metal found in meteorites and extraordinary mineral veins” but does not mention it being magical.
Xanathar’s lists the properties of weapons “made from or coated by” adamantine. These are distinct from the proprties of magic items. For example, adamantine weapons don’t get magic item resiliency.
Official Example (Spoiler Alert)
There is an example of such a weapon in official Wizard’s 5e material.
Note, the staff does not strike as a “magic quarterstaff” like the Staff of Power does. It is a magic item but not a magic weapon. As far as whomping things goes, it is a “nonmagical weapon made of adamantine.”
For mithral items, the rules say very little
I’m not aware of any mention of mithral in the core rules outside of the magic armor. A DM might follow the example of adamantine — that it’s a rare metal that is often found in magic items. Or they might rule it is inherently magical.
Magic Items are defined as such. Custom items are defined by your DM.
If an item is listed as a magic item then in general they would have the qualities common to magic items of their type. A custom item invented by your DM might have any properties.
The particular qualities of any particular item in your game are of course up your DM. Your character might (and probably should) learn whether an item is magical or not, and its properties, resistances, etc., by means such as an Identify spell.