Need advice with countertop backsplash and bathroom subfloor
I'm a beginner DIYer in the process of remodeling the kitchen and bathroom of an older (1962) house. While removing the old laminate countertop, the backsplash took some of the drywall with it. I'm trying to determine the best way to prep the surface for the new tile backsplash. Can I patch it with drywall compound, or do need to install a piece of plywood or some other backer before I can tile?
I also stumbled into a small problem with retiling the bathroom. After removing the old tile and about an inch of the mud bed, I found a very uneven gravel surface that was almost impenetrable. I plan to level the floor using deck mud, but will the the high spots from the gravel compromise the integrity of the floor (since in some areas with gravel, the depth may be less than 1 inch)? Even if having the gravel there is ok, am I be better off in the long term if I remove them?
The biggest problem of all is, I have 2 wooden floor beams near the shower pan hat are rotted through. Could this mean I have a leaking shower pan? How much work is involved in replacing the beams?
Here is a link to the pictures
Thanks in advance for everyone's help.