ToME: the Tales of Maj'Eyal

1) Are there hotkeys to switch between shop inventory and char inventory in the base game?
2) Is there a way to set animations to have constant speed regardless of the framerate? It seems that certain animations are affected by framerate (like, yellow portal "doors" and central sphere animations in the fortress) and certain are not (like, aoe melee attack of a rogue)
3) Can I enable an addon mid-game, or do I have to start a new game to take advantage of an addon?

You cannot enable a mod mid game.
Doing so would be worse than the Spellblaze.

I understand about game-changing mods (like, new dungeon) but interface-changing mods (like, better inventory screen, auto-transmog gems)? I thought it would be reasonable to allow it, leaving it to authors to decide if it's safe (like Skyrim, where some mods require new game, and some don't, but you can enable any mods mid-game)

Adding addons to an existing character is actually pretty easy, but, as stated above, there is no guarantee that problems won't show up, since most addons assume that they are installed from character creation onward. There is a risk (depending on the addons involved) of making your character unplayable.

To change the addons for a specific character mid-game:

Locate the character save directory.
Edit the file desc.lua in there.
Find the line that reads addons = {....} containing the list of addons enabled for that character and add or remove addon names in the list. (The names are the internally used short names defined in the .teaa file)
Reload the character.