I'm currently predicted BBE, can I get these grades up by January 2024?

I wouldn't recommend dropping any subjects this late to be honest. The amount of work to catch up on would likely be overwhelming.

As for the possibility of increasing your grades by January - nothing is impossible! If you find what really works for you, you have plenty of time to stick with that, until January.

Do you have any advice on how to revise for chemistry?

PMT pass papers, practice questions, CGP revision guides, find YouTube channels that you respond well to, use flashcards to test yourself on the spec,etc.

Make sure the textbooks or revision guides you use are based around your exam board as well.

Hard to say since it depends on your school's policies. It's up to them what they put down, some schools will give you basically whatever you ask for, others will stick to their guns and have rigid internal guidelines. Remember that even if your predicteds were bumped up, you would still have to get somewhere close to them to meet university offers: if you got predicted ABB but ended up with ABD that might result in you missing your offers and you'd then have to rely on lenience on the part of your firm/insurance, ideally not a position you should get into knowingly. (ie. I would dissuade accepting offers you know you likely won't meet with the idea that the university might be lenient, or at least having a very solid insurance if you do this)

Getting the Bs up to As would be pretty normal. For the E, it depends how much work you're putting in at the moment. If you're working very hard, getting it up to a B or A would be pretty aspirational, but if you e.g. did no revision for your mocks, then you should be able to get this up by just knuckling down.

You could restart year 12 with different subjects, this would not be unheard of. Trying to do a whole A-level in one year isn't impossible either, but might not be advisable unless there is an A-level you know a substantial amount of already. An equivalent qualification might be more realistic but you would then have to check whether the universities you want accept this. Would recommend talking to your school about this if this option appeals.

I've spoken with my school, and they're thinking on allowing me to switch to the BTEC applied science (equivelent to one a level), whilst continuing Biology and Psychology as I'm already pretty good at those two

Do you know how hard it would be to switch between A-Levels to BTEC and if it's doable in 1 year? As my teacher said it would be do able but I need a second opinion. Ty