8'x8' is a small room, but it is doable.
The 4" step up will not have a landing, but wouldn't be that bad because the step up isn't that high to worry. Just make sure that you watch where you are going when come out of the room.
IMHO, 2 2"x4" studs and 3/4" door frame is just enough for a door knob when open (Open in, door on one side of room would give you more room than open on center).
Go for a pocket door for more space if you can live with the corkiness of it, or get a sliding door/screen.
Get a book on basic construction from the library because it is easier to construct with guided illustration.
Tool:
Measuring tape, saw, hammer, nails (3" - 3 1/2" spikes), drywall, drywall screws, 4'-6' leveler, drywall, utility knife, pencil, chalk line is nice to have but isn't needed because the span can be cover by a full length stud, and drill & screws can be us in place of hammer & nails, and 2 packages of shimming.
See here for framing instruction; an easy way to make sure that your door frame square is to lay down a full sole plate across the door during framing (highly important if you want a none squeak/jam free door), then cut it off after the drywall is up (before install door frame). Do not nail down the sole plate where the door is going to be (pre cut 2 scores 1/2" deep off the under side of the sole plate where the door frame end so that it is easier to cut off before you hang the door frame, nail/screws 4"-6" back from pre cut line). In your situation you need only one 2"x4" stud on each side as corner studs, or 3 studs on 1 end of the wall and a single stud on the other side.
Good luck!