History:
over 30 years of property renovation i now specialise in bathroom design and fitting.
Answers:
Sad to say but who ever fitted the bath room must have confused the hot and cold feeds .i hope the pipes are easily accessible
A structural enginers report will be required as well as building regs approval .you will properly need a party wall agreement as well
If the tiling is level with the top of the aga and above ,no problem .aga,s are normally against a wall so it is not possible to tile behind them
Depending on the specification of the bathroom ,if possible its a must ,electric matting works well. but i like to use an overlay water system which works from the central heating system is only 18mm thick and can be tiled directly over very good result .