Yes, the metal is drip edge. Sliding it up under the first row of shingles (which should be a double-thick row, by the way, with the starter row being installed "upside down") is perfectly fine - just be sure you can get up there to nail it every few feet. It isn't bearing any load or anything, so it does not need to be nailed every 16".
Building wrap is used as a moisture barrier and to help with keeping air from leaking through the structure. You do not "need" to install it if you have no intention of insulating the garage. It wouldn't hurt to have it, however, because you never know if you might insulate in the future (assuming you don't do it now). The only reason it is installed before windows and doors is because you would typically wrap over the door and window openings and then slice the wrap in an "X", folding back the tabs before installing the window or door. This effectively ensures that the wrap will cover absolutely all of the sheathing.
Personally, I don't use the wrap - I will install a foil-backed foam core insulating panel system to add a little R value and provide the moisture barrier too.
If you're using vinyl siding, you should have a "Starter Strip" to nail to the bottom of the wall and snap the first piece into. If you don't, you can cheat by slicing the nailing strip off of the top of an extra piece and running that along the bottom. Or, you can install J-Channel along the bottom of the wall, set the first piece into it so that the bottom can't pop out of the channel, and just nail it. I will tell you that, while these shortcuts work, they aren't worth doing. Get the starter strip and use it.
Similarly, be sure you get the top rail pieces too. Again, you don't "need" this, but it makes the last piece on top of the wall that much more secure.
Base on your screen name, I'm thinking you're in my neck of the woods. If so, send me a PM and maybe I can stop by if I happen to be in your area for work and can give some tips (I travel into MA from time to time).
