Re: thinned joint compound
Jack is right.
The only time I've ever applied compound with a roller is when I'm trying to match a lightly textured surface.
For skim coating, you're still going to thin the compound slightly to make it more workable. If all you're doing is covering up existing wall texture to a smooth surface, then this will be an easy task. Work in strips as Jack suggests, as this will keep you focused on doing a good job.
Don't over apply the compound, you're going to need several coats anyway. Work a small area at a time, try to leave as few knife marks as possible, the smoother you get it while it's wet, the less sanding later.
Between coats, scr-ape the knife over the surface of the dry wall to knock down chunks and ridges before continuing, this will cut your skimming and sanding work down considerably by not having to smooth out new bumps and lumps you've created.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!