I was wondering what D&D 5e feat, class and race abilities would affect unarmed strike from this list.
Mage Slayer, Savage Attacker, Sentinel, Rage, Reckless Attack, Brutal Critical, Frenzy, Improved Critical, most Manuevers, Divine Smite, Assassinate, Death Strike, Savage Attack (half-orc).
If any of these wouldn't work with unarmed strike, would they work with a natural weapon from something like alter self?
Lastly, are there any spells that would improve your unarmed strike?
Anything that works with a melee weapon atack will work with an unarmed strike. Of the things you listed, these work with unarmed strikes:
Rage and Reckless Attack are special; they worky with any melee weapon attack that is based on Strength. So they'll work with normal unarmed strikes, but if you are a Monk and choose to use Dexterity for your unarmed strikes, Rage and Reckless Attack will not apply.
All Alter Self does is make the damage of your unarmed strikes 1d6 of the appropriate type, make your unarmed strikes count as magical, and give you +1 to the attack and damage of your unarmed strikes. It does not change the way they work in any way that would affect any of the above.
Spells that improve unarmed strikes:
