What's stopping you from getting GP/hospital work experience before you have to apply? As you do have some relevant experience, they won't immediately bin your application or anything, but it might put you at a disadvantage against people who have both hospice/caring home work experience and GP/hospital work experience. But remember work experience is only one of many factors they consider, so that's not to say you won't get a place, especially if your grades etc. are good.
Yes, you can definitley put helping your neighbour on your PS as long as you're happy to talk about it in an interview. Lots of things on PSs don't have official proof (I have read X book et.)