You will likely find that your new doors may be a little smaller than your old doors. Measure the distance between jambs at the floor (not including door stop). If it is, say 32 1/4 your new doors will likely cover that hole by 1/8 per side. You will likely have to jamb extend your new doors though. Older doors usually had a wider wall thickness than today's standard doors. Be sure you dont add the jamb extension on the latch/hinge side of the door... do it on the opposite side of the jamb. On your height, make them as tall as possible... allow maybe 3/8 on top for shims. Your jambs will likely sit on top of the floor... Check your floor for level and if needed, cut each side jamb to match the variation in the floor so that the heads will sit level.

Why use a solid core door for the interior? how much do you need to cut off of it?

I would replace the whole thing with a pre-hung. In the long haul it will be less work. And I also ask the question of the need for a solid interior door?