Although there was clearly a small crack at the exterior wall where the stucco meets the cement at the ground.Since rains like this are so rare (like, once every 10 years), is there some sort of caulking I could apply to the crack to seal it?

First a couple of questions, 1, What is on the other side of the cement wall?

However, there is a soft black material that has been glued to the cement floors and getting it up is proving to be a total nightmare.  

A bit of hydraulic cement patched it up correctly and it's doing fine now. 

Little did I know within 5 mos, she would fake disabilities to get $ from the govt, call code enforcement to make it that much harder to evict, and deface and damage the property (We're talking cement in the toilet tank and pickles down the drain type of stuff).

(studs should be near edge of tub to accommodate cement board to drywall seam) I used curved shower rods in all my rentals.  

But if you have an RV or equipment trailer you are storing on anything but a cement pad or blacktop you get a written warning.

You only get close to $600 for vinyl shakes and fiber cement or wood painted how ere detailed trim can add to the cost especially for Azek or equivalent.I would check your numbers.

Should these layers of adhesive vinyl be removed before installing the new cement board and ceramic tiles?

Wood lasts 7 years, composite lasts 20 years and cement lasts 50 years.