In my opinion, you should long rest at your camp at least three or four times before you even get to the Grove
Oh ... one can do that? I tend to do the beach, crypt, grove (without beach and tunnel), pick up Scratrch and Karlach, and do the owlbear mauled cultists before a Long Rest ...
Maybe I am just unfamiliar with the game mechanics. Do long rests set up this camp where dismissed companions are sent to?
Yes, the game sets up camp automatically.
Are there any timers that long rests works against? (things I can miss if I become a narcoleptic protagonist?
Not that I know off. Or that matter.
The only thing you should look out for is straying into the Mountain Pass area, as that closes several quests and storylines. But that game shouts "u so gonna get kilt!" at you when you try to go there :P
