I'm going to assume that the elderly person in question has full mental capacity and is in full agreement with this course of action when answering
could they use funds from sale of their property to convert our garage to a granny annexe? Or to add an en-suite etc?
Yes it's their money they can do what they like with it. In return would they expected to be added to the deeds/mortgage/have a tenancy agreement
If they lived with us how would they contribute to costs of bills/tax/house insurance etc etc?
that would be for you and them to decide between you. Neither party should feel they are worse off from the arrangement would be the ideal.
Who regulates this?
No one
What pitfalls do we need to be aware of?
What are the expectations of each side? Are they realistic/ match up?
Will they expect to be included in all of family life or will they want their own space?
What happens if you go on holiday?
What happens if you can't/ don't want to care for them any more but they refuse to leave?
Is everyone on board with the decision?
Who is going to take on the caring responsibility? How much are they genuinely willing to do?
It all seems complicated from what I read on here and I’m wary of how liable we’d be financially once they moved on either when they’d passed away or if they needed to go into nursing care
If they went into care and didn't own the (your) house then the local authority wouldn't have any claiming your property.
seems to be so many issues that I don’t even understand
Caring for elderly relatives is much harder work than most people appreciate. It really tests relationships. I would always recommend a test run before anyone makes a commitment.