Slugsie wrote:
[sorry, forgot this bit...]

The floor in the bathroom is going to be tiled soon, is it better to
sit the toilet on top of the tiles, or tile round the toilet?

In my opinion its best to tile under the toilet if poss..

Regarding your proposed toilet move.
Moving a toilet I find one of the more difficult diy jobs.
If the stack and pipework are cast iron it increases the difficulty;
although you can get clamp on adaptors to connect plastic waste pipe to cast
iron and they do allow some lateral movement.
You need to work out if, with a new hole for the pipe, there are suitable
couplers/bends to reconnect to the remaining outside sloping pipe easily.
You may have to use a swiveling adaptor.
The push in pan connectors also allow a few degrees of adjustment.