Can my friend do my UCAS reference?

Short answer is 'no'

It's a real shame.
Oxford (and some other universities) haven't previously been so strict around predicted grade requirements for resit applicants - it's something that TSR might want to take up with them as something that's costing applicants a lot of money and meaning they may miss out on good candidates who aren't able to pay for predicted grades from private tutoring organisations.

It's also worth raising with your school and explaining that because they're unwilling to provide predicted grades (even with caveats that those predictions are based on your own target grades and not based on the school assessing your current work) that they've prevented you from applying to specific universities. They may well be willing to revise their policy especially now the UCAS reference has been revised to let them make this clearer.

Personally, given the lack of consistency and accuracy of predictions, I have said for years they should be removed from the UCAS application altogether and universities should make judgements based only on achieved grades, PS, reference and the mix of qualifications (plus interviews and entry tests and other information). There's zero risk from a university making an A*A*A* offer to someone predicted DDD. If the applicant gets A*A*A* then they're getting a student who meets their academic requirements, if they don't then the university doesn't have to take them.

I was told I could take my exams and reapply for 2025 but that seems like too much to me. I don't really like taking a gap year. I only did this because my results were far below what I know I can achieve and I want to give it a proper go and have no regrets. It seems silly to take two years off for something I can do in one.

I've always thought the UK system was kinda silly in that regard. We need an impartial system that works for everyone. Unis seem more lenient with mature students but that doesn't really mean much for students like myself aged 18-19.

Sorry, i don't understand what you mean by "They may well be willing to revise their policy especially now the UCAS reference has been revised to let them make this clearer". How has UCAS been revised and why is that important?