I don't think income tax is applicable if anything it would be a capital gain I would have thought. You'd need a decent tax accountant to give you a definitive answer on that one.
No idea about the nursing home question but if they had a mortgage over the property then that would be registered as a charge and repaid so I can't see why yours wouldn't be - the length of time between buying and having to sell might be important though ie. if it is soon after the event then it may look like a scam to get round the rules.
CGT only becomes payable when you sell something so if your parents sold to you you would acquire the asset at the market value at that point and CGT would start from that point. It would be better for tax purposes to leave the property in their names and crystalise the charge when they sell it (or it becomes part of their estate).