How is the house’s foundation constructed

The answer to your question is that there is no answer - there are just so many variables that it's really impossible to answer with anything quantitative.

The biggest variable is how much water is going down the drain. If you had a clog but very little water usage, it could be days before you saw anything on your basement floor. If you have a family of 8 taking showers every day it will show a lot quicker.

The smells start being noticable when sewage starts backing up on your floor, until then its unlikely you'd notice anything. Again, this can vary. If you are just putting fresh water down your drain, it might never smell. My neighbour didn't notice until they had several feet of water in their basement!

The rate of deteroiration will depend on age and condition of foundation beforehand, temperature, soil conditions, what the house was built on, quality of construction, thickness of foundation, etc.

In the aeronautical industry, we have this saying "If it looks ugly, it flies ugly" which has proven out in that aerodynamic design needs certain sleek lines and cobbled together garbage just doesn't have what it takes.

Same goes for the building industry. Despite the cosmetics of Stucco and the willingness to absolve the builder because it "doesn't look pretty", if a non-load-bearing wall is this foul, you can be certain that little or even less care was taken on the structural elements of the building.

This is why a 6.5 earthquake in a country with strict building standards can be fairly annoying but in another with unreinforced masonry and no standards, ends up killing 30,000-40,000 people, both areas having the same population density.

Poorly designed, non-loadbearing walls will just shear off the building and fall into the street in a quake.