Wanting a new bathroom installed

As above, you can have some serious issues with soil pipes if your relocating out of reach of your soil and vent pipes. There are a number of macerators on the market that will suit your needs if you do struggle, but they can be costly, and children can tend to put things in the toilet that totally destroy them and add another cost to replace and depose of. Personally i would not use old heating pipes as potable (drinking) water supply in the basin, its definitely not sanitary, and its pointless to install a separate main for just on connection. They can be utilized for hot water depending on your system and the state/age of your pipework, however, but they would have to be isolated from the remaining heating system anyway, and its probably just as simple to install new. overall, these types of projects are achievable as there are a lot of equipment options.

You can’t use radiator piper as these are flow and return pipes. You will have to Tee into an existing cold/hot and run the feed to where it needs to go :)

Yes you can and i have done "just that" many times before. Just watch out for leaks on joints once mains pressure is applied.

If moving bathroom into bedroom you have hot and cold pipes to take from old bathroom and relocate in new positions . The waste pipes usually are the hardest to get to new room . The toilet pipe being the worst .The only pipes in bathroom that can be used and staying are your radiator pipes . You either keep radiator were it is in old bathroom or relocate to your desired position . So it's workable depending on amount of moving pipes and floors etc