They eat through the cement cinder blocks and move up the walls to make nests.

If you already have a nice and solid cement floor tile it.

It looks like someone tried to patch with cement and foam.

Mortar is a bond-making material composed ofmeasured amounts of cement, sand, and water.

For example:  all my properties are on cement slabs.  

Being in the second highest city with the worst foundation issues, would cement piers do better or just regular pier and beam?

I'd leave the tub, it looks fine - then just demo down to the studs, redo the tile (cement backer board, sealer, tile, grout, adhesive) and faucets/valve and move on with it ($200 in parts).

The house is made of cement (Also cement roof) , and it is a 4 floors building - Still in warranty from the contractor (In Israel they have a 7 years warranty and they will fix any damage to walls roof and so, Also the one in the 4th floor is responsible to the roof after the warranty   ).

Here in NYC, 3 families require fire escapes, cinder block or cement wall furnace rooms, not required for 2 family.

Ask yourself if you were a billionaire, concerned on how you cement you position of generations to come, what would matter to you, then review.