I can't speak to the tile, but how about taking down the medicine cabinet/light bar and replacing it with a simple mirror with two scones on either side. I am in the process of doing the same thing in my bathroom and I found a pretty round mirror and two polished nickel sconces. I also bought a small matching glass shelf to put under the mirror. Very elegant. I also think clear shower doors will open up your room. They are easy to care for if you "squeegee" them after each use.

It's not likely you can just "pop off" the tile. You'll need to do a full demo and put up new cement board to tile over. Certainly doable, but messy and time consuming. Worth it? Only you can decide. I'd personally say yes, but then we're redoing every last thing in our entire 13-year-old house, so I'm a little crazy that way.

Just a warning, deciding to tile will be the first step in deciding to completely gut and redo your bathroom. Tiling in and of itself could be, I guess, done at a reasonable cost. The thing is, you'll already be pulling out all the gypsum board and lord knows what else is covering the studs (hopefully not revealing rot or mold along the way) and replacing it with cement board... so while your walls are open, why not add electrical, why not change plumbing, why not get that crazy shower setup you always wanted, what about a new vent fan, etc, etc... tiling is the gateway drug to a complete bathroom remodel. If you are still thinking cheap and temporary fixes, I would look into having your tile "refinished" or covered with a new tub surround. There are many companies that are in the business of these temporary bathroom fixes. I think the price range tends to be around $1,000ish, where as bathroom remodels average around $8,000ish.

only you can decide how much demo you want to do. One thing I can tell you- it is always much messier, expensive and time consuming than you originally thinking. Once you start "popping off" those tiles... all hell will break loose and you find yourself in the middle of torn apart bathroom. who knows what is underneath those tiles and in what condition.
Regarding marble- I know lots of people put in the bathrooms- not a good idea unless you have cleaning service IMHO. Powder room ok but not where real life is- too much maintenance, my life is short enough to spend rest of it cleaning my bathroom. Marble is soft and porous stone- try cutting it with a wet saw- goes like butter as compare with many ceramics/ porcelain which you can not touch without special diamond blade.