Drywall – How to safely work in the attic without a floor in place

1. You can, but there's a few issues to be aware of. First, your blown-in insulation requires space to stay "fluffy" and work well. Compressing the blown-in with batts will diminish the former's effectiveness and compromise the overall r-value.

   Secondly any vapor barrier (the paper on the roll) should be against the drywall. If you don't have a vapor barrier in place, I would address that (see this article from this answer for more info). If you do have a vapor barrier, make sure you buy unfaced (like your link), or remove the paper from your batts before installing.

   Your best value will likely be buying more blown-in insulation. If you buy a reasonable amount most of the big box stores will let you rent the machine for free. It is a messy two person job, however.

2. It looks like you have standard 2x4s on the edges where the drywall is attached, you could staple faced fiberglass batts to it. Measure between the "studs" and buy a roll that you can cut to width. I've seen skylights both with and without insulation, I don't know if there is a downside to insulating them.

Edit

If you put plywood over the cellulose, you're going to have a similar compression problem. This table shows you what kind of r-value you can get per inch. So the depth of your joists (they didn't look very tall) is going to limit the r-value you can get if you're covering the joists with plywood. Since it appears the insulation you already have is near the top, you won't see a huge gain in efficiency if you add just another inch or two of blown insulation. You might try asking another question once you figure out what r-value you have and what r-value you'd like to have. If you're near the recommended r-value for your climate and your house is still too cold, you might be better served by looking for air leaks first.

Nope, it shouldn't cause problems with moisture buildup -- but how much blown in fiberglass do you have up there? If it's less than your roof joists, it's not enough, and you should think about adding some (or a lot, actually) to bring you up to R-30 at the least in your attic.

If you do have that much up there, but you moved some to the side to put down the OSB, you committed a minor home improvement sin and you should pull up the OSB, put down some 2x6's crosswise to your rafters, and then put the OSB on top of that.