Agree with the comments on the tiles - take them off!
If you remove sanitary fittings, you may need to replace traps etc. Don't try to reconnect using the old traps, without at least replacing sealing washers. You will definitely need a new pan connector. The seal on the old one will die when you remove it. Get one the same as the one you've got. That is to say if it's a straight connector, get a straight connector to replace it. I like the ones from Screwfix, not because they're cheap but because they ALWAYS seal. That seal is so tight that it hasn't got a hope in hell of leaking. I've had some that wouldn't seal from some merchants, and there's nothing worse than a leaking pan connector!
Sealing washers for traps - 32mm for the sink, and 40mm for the bath.
If you fit new traps (and I would suggest you do) you may have to alter the waste plumbing to accomodate the new traps.
Yopu will also need a new donut washer to seal the cistern to the pan if you separate them., if it is the older type of connection that uses a bracket, you may want to replace the whole lot. You can get these kits from merchants. If it's the newer version that work with two bolts through the underside of the unit, you may need to change the kit. The washers don't like being used a second time. Having said that, you may be able to get away without separating them.
If her suite was installed professionally I suspect you'll have solvent weld fittings. Otherwise you could have a mixture of solvent weld and pushfit, with compression fit in between. Solvent weld and pushfit wastes are NOT compatable. When you go from one to the other, you'll need a compression fit coupling between them.
Hot and cold supplies - It is a good idea (and also complient with regs) to fit isolating valves to the taps and the cold feed to the cistern. It may be a good idea to put these in whilst you have the sanitary fittings out of the way. People usually fit those ballofix type valve that operate with a flat screwdriver.
As far as physically removing the units from the walls, I suspect your kit will be screwed to the wall but there are an increasing number of ranges that are designed to be siliconed to the wall. If these are then simply slice down between the fittings and the wall with a hacksaw blade or similar to break the seal. Then you can clean them up.
Good luck, and ask again if you need help. I'm doing a fair few bathrooms at the moment.