Staying longer in Italy

1. Would he be able to sponsor me as a family member even though he is there and I am in Italy (since they are both EU countries)?

Simply said no. A nephew can only be considered a family member in limited cases and you would have to live with him/he would have to reside in Italy for this to be relevant under EU law.

2. At the moment I'm on a gap year (unemployed) so e.g. I were to apply for a long term stay visa, if I have a letter of acceptance from an institution in SA (evidence that I won't immigrate) would that help my application to be approved?

That's a start and probably necessary but far from enough. In fact, having no intent to immigrate is usually less relevant for long-stay visas (as opposed to short-stay visas). You also need to find a long-stay visa you would qualify for and could apply from within Italy (as opposed to returning to South Africa first). I don't know whether Italy offers this but I know many EU countries don't.

1) Would he be able to sponsor me as a family member even though he is there and I am in italy (since they are both eu countries).

If you are asking about family visa type of sponsorship, a UK citizen can only sponsor you for an UK visa. This visa will not allow you to stay long term in Italy.

I'm also unsure whether an uncle can sponsor you for a family visa; gov.uk says doesn't mention siblings for family visas.

But if you're asking about general sponsorship, such as if he commits to support you while staying in Italy, then yes, he can do this. Note that in this case it won't be a family visa, and you'd have to satisfy other conditions for a long-term visa (study, work etc).

Also prepare to address extra hurdles, as sponsorship applications stand on weaker ground. This is because in addition to evaluate your circumstances, the circumstances of your sponsor have to be evaluated as well, including understanding whether he's capable to support you, and how likely he'd to drop his support if his circumstances change.

2) at the moment Im on a gap year (unemployed) so eg I were to apply for a long term stay visa, if I have a letter of acceptance from an institution in SA (evidence that I won't immagrate) would that help my application to be approved.

This would be better than nothing, but this would be a very weak evidence, unless this requires a major commitment from you. For example, if you have posted a large deposit which you'd forfeit if you do not start attending courses, this would be solid evidence. But if it is just an acceptance letter which you can throw away with no financial consequences, this is not strong evidence.