Has anyone ever tried to carefully remove the 50's ugly bathroom wall tile and use the same base to install updated tile?. Not looking forward to ripping out all the tile and the inches of mortor behind them... it but it would save me some cash and time... is it even possible?

If this is ceramic it is likely set in modified thinset which is hard as cement. When the tile is popped you will need to scrap.chisel the surface fairly smooth before applying any new tile.

UNfortunately removing tile is not a precise or easy job. I have renovated many bathrooms in my history of work. I have always found it to be the easiest to remove everything on the wall. Rarely is this a load bearing wall so it is easy to remove and replace. Once it has been removed(leaving pluming in place). Once you have the walls replaced use the recommended underlayment/wonderboard which is easy to cut and fit into place. Once this is completed you can begin installing the new tile of your choice. You can use a thin set mortor or a quality mastic made specifically for ceamic tiles. Gl and take your time.