I got nice solid core prehung interior door. It seems to have pretty weak frame, though and I see that hinge screws are protruding through it and the door is attached to the frame with nails on opposite side to prevent swinging. When I removed those nails, door weight immediately skewed the frame. So I put those nails back for time being but I will have to take them out before install and likely unscrew hinges at least partially.

In addition I have 1+" wider opening than this frame and I would like hinge side to go as close as possible to stud. This leaves me with 1" gap on the lock side and I plan to put 1x4 there.

All in all, it seems that a lot of things that need to happen to install it right, so I am wondering if it's advisable to just remove door from the frame and then install frame level, plumb and square where I need it and then reattach the door with 3" hinge screws. That would make my life lot easier but I've read in some places that it's difficult to install the frame right without a door. Not sure why.

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Update.

I removed the door from the frame and also removed side stops from the frame (they were only attached with few staples). I penciled where stops were. Then I took my time to level, square and plumb the frame in the opening paying especial attention to get exact distance between jambs at the top and at the bottom. In process, I cut jambs at the bottom to make top of the frame exactly level. Working with just frame was fairly easy as it is very light.

To keep it in place I used 2" #6 trim screws placed where the stops are and recessed below the surface. Started with area above top hinge. Shimmed everything right and placed few more of those screws above and below hinges making sure they go through shims. Screws were good as I had to take them out and replace couple of times before getting things to my satisfaction. I only used screws on sides and left top shimmed but with no fasteners.

After I was done with screws, I marked their location to avoid putting nails in the same spots.

At this point I used air shim on the floor and my wife's help to prevent door from falling to align hinges on jambs and screw them back in. Double checked everything and then nailed stops back with 2 1/2" finish screws. Did use it on sides and at the top while making sure that nails penetrate shims.

Voila, door is seems to work great! One little thing I would pay attention next time - I attached hinge side stop a bit too close to the door, so it's getting a bit tight on the last inch before door is fully closed. But it seems acceptable so I decided not to redo it, Will do in future if really bothered.