Flooring Tile - Ceramic floor and wall tile in bathroom

Circa 1955 house with original ceramic wall tile and non-original linoleum tile, which I believe may have been put over top of ceramic tile. Wall tile still looks pretty good except for slight bulge outward in a couple places. Wondering if I should tear out the whole bathroom floor and put in new plywood subfloor and build it up. And, not sure what to expect in wall, but hoping there'll be no surprises. Best to take out old material and apply tile to new stuff, or is it okay to "patch" what's there?!

A first for me. Luckily, it's a small bathroom, and I hope to do it right but not go overboard. I tend to make things tougher than they ought to be on projects like this.

A small bathrm, I'd gut it & start over, because in my experience, it's just alot easier that way, and you can update the plumbing & wiring while you're there & put in ventilation. But a 1950's tile job, that ceramic could be set in a mudbed, if so & it was done right, be prepared, might be alot of work tearing it out. You really need to see, what you're up against, if there's any loose tile, I'd do a little more investigating what's there underneath the tile.

Thanks! That's pretty much what I was thinking but was hoping someone would say sand down some of the stuff there on shower/tub walls, apply cement or something, and attach new tile. I think the floor was torn out years ago, and, yep, it was tough to do that. As best I remember (I was a kid) there was wire in plaster- or cement-looking stuff. I imagine that may be what is in the shower/tub walls.