(Even though in these old buildings the floor is sometimes so thick that and made of "blue" concrete that is would probably hold without footings, but nobody can guarntee that).But that alone will not correct the sag. 

It looks like lathe and plaster which means the walls are most likely a thick mud wall with plaster embedded with wire which is a bear to remove, hopefully that quote is for a full gut and replace, but I would just update the floor, have the wall tile painted, tub glazed, new shower fixture, vanity and accessories like towel bar, shower curtain. 

They may try to get arrogant or annoyed that you are making that much, you just need to have a thick skin.

I've been using Lifeproof from HD and like it's thickness, flexibility and soft feel when you walk on it.

If you have 1" thick filters I would change them monthly.

Drywall thickness, wrong type of plumbing, etc.

If don't buy a home in a flood plane or in the thick grassy areas of CA then the only work you'll being doing on your rental is to walk from you home to your mail box to pick up your monthly rent check.

When she moved in I had installed a new 4-inch thick filter in the air handler.

For each transaction here in California I had to sign a stack of documents two inches thick.

There are many different options when it come to vinyl, the most important of which is panel thickness, which ranges from .040 to .050.