Joe-the sink and toilet should be lossened enough to lift about an inch or so,just enough to slide a cut tile underneath-any more movement and it may damage the drainage pipe on the back,especially with the toilet.
You can cut groves in the tiles so they slip around the holding bolts and allow the toilet/sink to sit on top and be re-tightened.
As for the shower this can also be disconnected and tiled behind, but if you want to take it off fully I would consult a plumber and sparky-when you go to re-attach the unit make sure you have a quality drill and the proper tile drill bit which any hardware shop will supply you.
Mark out where you holes will be drilled using masking tape and a pencil as this also helps to prevent chiping and cracking of the tile.
I'm an amatuer learning from my mistakes and no pro but I would give it a go myself if I were you-to get a tiler in costs about 20 to 30 euro's a sq yard.