https://www.citizensadvice.org.uk/family/if-you-were-living-together/what-happens-to-your-home-when-you-separate/
It all depends on if you are keeping the house? You’ll need a solictor to transfer the house in the persons name and to transfer any monies owed to the other person. If you are selling you will need to arrange with the solicitor what you are both doing in regards to money being returned to yourselves.
I don't know where I'd live if we split up so it's not as easy as just putting the house up for sale
No idea but I would contact a solicitor to be honest. It would depend on whether the house and mortgage were under both names or not.