Can I replace the existing slab door from house to garage that is 1 3/4" thick with a door that is same size but only 1 3/8" thick? If so, what modifications do I need to make to the door frame if any?
You do not want to replace a 1 3/4 inch door (which is presumably a solid core door) with a 1 3/8 door of any type. The reason is that fire codes require a door with a fire break rating between the house and the garage. Fire break doors are generally 1 3/4" thick for standard doors.
Many homes now days may even use a steel clad door in this application instead of just a solid wood door.
First, you may need a smaller set (or different set) of hinges, should they protrude from the outer edge of the new door, due to alignment issues. Nothing quite like a nasty scrape while walking through the entry carrying groceries to invoke a few special expletives when the bag tears open and drops the carton of eggs on the floor.
Should the holes and door align with the hinge edge with the same distance as the old door, then your new slab door will move "away" from the hinge side of the door, by that 1/8", and in turn, your strike plate's 'sweet spot' may need to move an 1/16" away from the hinge side of the door. That can be tested and verified once the door is up.
If you do have to replace the hinges, your trim around the door jamb (where it meets the door) may need to be shifted inward, so it meets up with the door again. As Stanwood mentioned, you can usually just put on larger weatherstripping instead to make up the spacing difference. That is a lot easier than pulling that trim, relocating it, and then repainting the entire jamb.
No matter what, keep your small chisel at the ready to clean up around the hinge placement, as well as chipping away some extra room for the strike plate holes - especially if the deadbolt doesn't align quite right.
Yes. The latch is centered on the door so the new door will sit imperceptibly at an angle when latched. You will want to confirm that weather stripping around the door provides a good seal. It should notvbe a problem to achieve this and in any case when replacing the slab it’s a good time to consider replacing the weather seals.
Garages are to be separated from single family residences by 1/2” gypsum board on garage side ONLY, provided the garage does not open into a sleeping room. (See 2017 edition ICC Table R302.6.)
Also the door between the garage and house shall be a solid wood door a minimum of 1 3/8” thick and is not permitted into a sleeping room. (See ICC R302.5.1.1.)