Cat litterbox (housetraining?) question

We are currently trying to figure out the best place to put a litterbox in the house. It is likely going to end up in the closet of our spare bathroom, but I had an idea, I just don't know if it is plausible.

Can you teach a cat to go to the door when it needs to go to the bathroom? Currently we have her litterbox and bed/food/water in the garage, as we leave her out there when we aren't home/at night since we don't want Abrams and her to be together unsupervised. During the day we've just been periodically putting her back out in the garage to give her a chance to go to the bathroom. If we keep doing this, will she eventually signal when she needs to go out? (Like a puppy?)

If we could continue to have the litterbox in the garage that would be FANTASTIC. But because it is a rental, we can't install a cat door in the door to the garage like we originally wanted to do. Boo.

All of my parents' cats use the bathroom outside and they just go to the door when they have to go. I think she may have one litterbox in the laundry room, but it is never used. I just wasn't sure if it was possible to pretend "outside" was a litter box in the garage. lol

I think it could work so long as he doesn't have anything that he feels is a good alternative indoors and you act quickly enough when he's at the door. I'm not sure if he'll ever learn to signal at YOU, as in "asking" to go out, but you'll likely notice him hanging by the door wondering how to get out there because he's got to go and knows the toilet is out there.

No idea, but would it be possible to get a door, add a cat door, and replace your current door to the garage with it? Then there's no damage to the rental door, but you still get your cat access!

I don't think it's a good idea. Cats are perfectly willing to improvise if their litter box isn't immediately available.