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The easiest way to ID weedy grasses is from the inflorescence, the seed producing stalk. Compare your weed to Dallisgrass, you could also try asking on the grasses forum or Name That Plant. Good luck!

Gosh, I'm not an expert but 4 x 4 ought to be OK. When you think about it, old time strip hardwood went down over just a subfloor so I don't see a problem. Other than it may be a bit more difficult to stagger seams just because you'll have more of them. No doubt full sheets would be preferable but sometimes you just gotta' do with what you have. Another thought--maybe rip the sheets lengthwise and put down 2x8 sections? Easier to handle than a 4 x 4?? Yes, you can do without the glue. I followed instructions that I found from some experienced floor guy on the internet somewhere (it's been a few years ago) and did the glue because my subfloor is only 1/2" plywood with visible dips and sags between joists and because the old floor was a squeaking nightmare. Also, it is a large high traffic kitchen/ great room where we removed two partitions and where squeaking would annoy me all day, every day. You're dealing with a bedroom, maybe even a spare bedroom? I had to sift thru a lot of information to even find how to deal with my situation of having only 1/2" ply. Sure wasn't up to removing it and having to walk on joists to install a thicker subfloor. The glue was extra insurance. Oh--I know you said that you knew to stagger seams; I assume you also know that the second plywood layer goes on perpendicular to the first layer? Mentioning just in case... Not something we do everyday so it's easy to forget even stuff we already know!

I know about Georgia summers. :). Have you considered just putting that area to lawn? I would suggest pricing out weed removal and sodding. If that's too much, weed whack it down, moisten a bunch of cardboard and cover the areas with cardboard and a bit of mulch to weigh the cardboard down. Leave it over winter then pull back (weeds should be smothered) and seed in Spring. Grass is really the easiest as mowing will make quick work of anything that attempts to grow bigger than an inch or two. If you want your garden beds back, do the same smothering method except don't pull anything back in the Spring. Just makes holes and plant. Put thick layer of mulch after planting to discourage weeds (not right against new plants). I'm thinking if you don't get out there occasionally to weed or if you don't renew your mulch yearly, your garden beds will run wild again in just a few years.