Bio, chem, and any other would be good for all of those options except chem at top unis. Oxford, for example, requires maths, and I can tell you from experience that the course is very maths based indeed. Further maths is also a recommended subject for that course.
For medicine you don't necessarily need biology any more. It does open up options, but there are ~18 med schools that don't need it. If you didn't want to take it, and doing so would either threaten your achieved grades or limit your other options, you don't have to take it.
Yes, she is. Firstly, why would you have a requirement without saying it. That makes no sense. Secondly, Oxford releases
extensive stats including on this topic. There is in fact a trend - a correlation that is mainly with BMAT results actually - but there are students who get in without maths, so she is wrong.
In you look at other unis, other subjects actually
correlate better with offers than maths though.
Well... the way you've phrased that... depends what you mean by hands on teaching! Oxbridge would be better for small group teaching clearly, with the tutorial system. But if you're wanting an afternoon per week in a GP surgery or hospital right from the beginning, better pick elsewhere for sure.
Oxbridge is very unique in a lot of ways so its good you've visited, but definitely visit some others before applying.
Wow why was she so rude to someone wanting to do her subject?!
I mean, that is not exactly the best plan! You're saying you literally want to let this life-changing decision regarding your lifelong career just to pure chance lol?! Throw the dice in the air and see which uni you get into?! You should really put the effort into making that decision before you apply to uni. If it takes a gap year or something for your to make up your mind then so be it - this is your entire life!
Besides - you may find that good unis for chemistry are put off by a medicine personal statement, and med schools would definitely definitely be put of by a combined/chemistry one.