Installing a Door in an existing pass-through
Personally, if it were me, I would buy a prehung 28" door and install it there. Less expensive and much faster than a custom door job.
To determine which swing to buy (left or right), back up to the hinge side that you choose and whichever hand is on the side of the way that you want to door to swing, get that.
You can shim out the framing with 1X4, as necessary.
To install it, you will need a level, a carpenter's square, hammer and/or screwdriver, and beveled shims (smooth cedar roofing shingles work great).
To make sure that the door swings clear of the floor, raise the prehung frame up on blocks (1X or 2X, depending on how high it needs to be raised in the frame to the header.)
Remove the door from the frame, and hang the hinge side first, making certain that it is plumb and square before nailing it. Push two beveled shims in from opposite sides behind the hinges to plumb it. Then do the top, making sure that it is level and square, and then do the latch side plumb and square.
The bottom of the door should swing 1/2"-5/8" above the finished floor (carpet, tile, wood, etc.).