Warning! Spoilers ahead!
In Let’s Go mode, when you press the “R” button, it sends out your lead Pokémon to walk alongside you. While in this state, your lead Pokémon can fight with other Pokemon, and pick up nearby items. The damage calculation while in Let’s Go mode has your Pokémon (essentially) has you Pokémon use a “tackle” of some sort of their type. This means type advantages have a big role on whether you win or lose auto battles. You do get less EXP than you would if you fought that Pokémon normally. Now, for evolutions, you generally have to keep that Pokemon out in the Let’s Go/Autobattle mode, (whatever you want to call it) while walking with it. For example, to evolve Pawmo into Pawmot, you must have it out in Let’s Go mode, and walk with it for 1,000 steps. You also have to do this to evolve Bramblin into Brambleghast.
Hope I helped! If you have any questions, just ask me!