Can I put new bathroom tiles on top of very old ones?

Removing the old tiles won't cause any cracks as such, but it may well pull off some plaster, but this can easily be repaired before tiling again. If feasible, you can tile on top of tile, but make sure you use the correct adhesive. Hope this helps. Bob.

Going over the top of tiles is quite common now days providing you use a good additive and grout. Living in a council flat makes no difference. What the walls are made of does, if the walls are very thin then taking the old tiles could cause damage. If in doubt get another quote and more advice before commencing the job.

Very unlikely, should be a simple job.

It depends on how roughly they are removed and on the type of wall between the bathroom and the hall. A decent tiler would have a multitool with a blade for removing tiles and this can remove tiles and minimize risk of damage.