How does sneaking work, if I have companions with me? Can enemies spot my companions and become hostile, even if they cannot detect me? What if I have e.g. 100 sneak and my companion/s have a very low sneak skill? How do companions (I usually take Cass and Rex) influence your chance to successfully hide from and sneak attack enemies? Thanks

As a rule, they wreck your sneaking, especially when you've built your char to be good at it. They're worse and their behaviour isn't scripted to sneak effectively. Only exception might be when you're sneak-sniping and have Boone with you. That works ok sometimes.

Can I take companions just for their perks and just leave them behind ("Wait here") indefinitely? Do I still get their perks, even if I'm on the other side of the Mojave?

Not sure about the perks. I don't think they'll wait indefinitely anyway. Maybe someone else can clarify?

Just checked it out. I let Cass and Rex wait in Freeside and fast traveled to the Mojave outpost. I still have the DT bonus on Whiskey and the Search and Mark perk from Rex. I know, after a while (days, weeks?) they leave and go back to their original spots. Never had that, but I think I'll just need to rehire them.

That's ... odd. I mean, you get the perk while they are miles away. Hm. I don't think I'll use that, kind of exploit-y.

It's three game days, the same as the creature respawn rate.

I'm not sure, but I think if you have companions wait for you in the Lucky 38, but don't dismiss them, you keep their perks and they never go back to their original spots.