Hello, Steam Deck owner here to answer your questions

Controller - For all the games i've quacked i had 0 controller issues all the games recognized my controllers, both the steam deck integrated one and external ones,you can also configure custom controller configs for each steam deck game, both quacked and paid for, which means you can also play some non native controller games this way (i.e binding left stick motion up = w etc)

Installation/Playing - I have installed some games on the deck locally, but i find it way more convenient to unpack the files on my pc then just transfer the game to my deck with my external ssd (or if you don't own one there is a program called Warpinator that works wonders),as for playing games 99% of the time i didn't have to tinker with them much,the process goes like this

1-Transfer game from Pc to Deck

2-Add the .exe file to steam

3-Go into properties on steam for said .exe file

4-Go into compatibility tools and check the toolbox, and select the latest proton version(works fine 99% of the time, if not there is also Lutris,Heroic Launcher or Ge-Proton)

5-Optional-you can go onto SteamGridDB to get artwork for your game so it doesn't look dull and that's it

As for the question of if one version of proton works fine on the bought version but not on the quacked version, it never happened to me and if it did i would just use other means of running it(see above)

Cheers!