On a hollow core door, how wide is the wood underneath the Luan?

Sounds like trouble. If this is a new door, simply look on the top edge of the door. The side styles should run through, the top and bottom rails mounted/ installed between. You should be able to clearly see that taking 3/4" off one side will leave you with next to nothing for either mortising in your hinges or the backset of the door knob. If this is going to work at all you should take 3/8" off each side. as far as cutting 1" off the top, you are better off taking 1' off the bottom as you need the strength and stability at the top of the door to strike the door stop, or half off each - top and bottom - as there is probably no more than 1-1/4' of wood in the frame. Scribe your cuts across the grain with a utility knife and cut on the waste side leaving just a hairs width to that knife cut to sand to.

The assumption here is that your are cutting a door to use as a door, not a dining table or base for a model train layout. :)

Professional finish carpenter.

Luan Door

That's to much to take off......your door won't have much strength left. Plugs at top and bottom of door are 1 1/8" and sides are 1".

You need to go to a solid core door.

Usually made with 2 inch wood frame. You could just get away with the trimming you want. Tape over the cut lines to reduce splintering.

one inch and a quarter cardboard in the center the same on the side styles

no problem