Re. removing the tiles - if they are fixed firmly or even very sloppily to the backing wall, they will bring off chunks of plaster as you remove them.
However, taking off all or most of the plaster and replacing it with a gyproc-type plasterboard product, and properly prepping this surface, would give you a good level surface to tile anwew.
This is a biggish job.
But I feel you want a nice quick fix - now, retro is in - how bad can 'brown tiles' really be? Can't you accessorise, smarten up the grout - I've seen loads of muddy brown tiling with white suites and it looks just grand to me.
Tile paint, as suggested by a poster, works OK if kept perfectly dry.....