I have 2 questions: 1 easy and 1 hard!

Easy first.. .
We live in a 2 story walkout [on a hill] 50s house & the water in our upstairs shower/bathtub when taking a shower can get very cold if the washing machine &/or kitchen sink is also using water.. . Is their some sort of diverter to aleviate this problem?
I do not remember this problem in our last 70s house.. .

Now the tough question.. . The lower level/basement/cement slab has a bathroom with a "formed" shower.. . The floor of the shower shell does "bounce"/just a little.. . We have been told that the leak is due to the installation.. . possible using plumbers putty, a common practice, but now known to cause this problem.. . Bottom line.. . The leak first showed up after a shower in the wall adjacent to the shower and then following into the next room closet under the rug.. . we stopped using the shower.. . However, months later, I put a garden hose about 3 inches down the drain and ran water for some time with no leakage.. . Is it possible to fix this without pulling it out and replacing everything?

I currently have screwdrivers pushed/wedged in between the shower floor and esposed metal frain rim.. . Thinking I might be able to squuze in silicone to plug and leakage.. . nder the drain lip in the

Thanks for any help you can give me.. .

Your temp rpoblem is due to a volume issue likely caused but improper pipe size. There just isn't enough hot water flowing to support the shower and other fixtures at the same time. The fix would be to increase the size of the supply pipe to the heater and the pipe exiting the heater to the fixtures, no small task. That supply should be 3/4" going in and out, what do you have.

The other issue is the base of the shower is poorly set and allows deflection. That will not be fixed by caulking or anything short of taking up the pan and doing it right. Shower pans need to be set in modified thinset or other similar material. If your floor moves it is not properly set.