Hello, these are just my thoughts on the above:
Firstly, congrats on securing two VSs in your second year - that's an amazing achievement and I'm sure these two experiences will help you in future VC/TC interviews.
Self funding the SQE v gaining legal work:
Personally, I would look for legal work experience over self funding the SQE, just because the SQE is still in its early stages therefore firms may want to put their trainees through a tailored version of the SQE. Gaining a TC first is likely to mean that your future firm will pay for your SQE course, give you a grant and you'll get to study with future trainees at your firm.
The main advantage of self-funding the SQE is that once your TC is secured, you may have the opportunity to be put in an earlier intake.
Answers to the questions above:
1. If you're looking looking at firms which do offer training funding/grants, I don't think self-funding the SQE would increase your chances of securing a VS/TC. When firms are interviewing you, my understanding is that this isn't a big factor.
2. You do have legal work experience - you have two VSs 
. There are plenty of legal assistance/paralegal/doc review roles which don't require any work experience. A lot of these roles are advertised on LinkedIn.
3. Same as above - personally, I wouldn't self-fund as this doesn't increase your chances of securing a VS/TC (but others may have different advice).
4. You can still talk about everything you have done in university on the TC/VS apps you send out. You can always get involved in local sports clubs, volunteer opportunities and there are loads of organisations you can get involved with to increase your commercial awareness (Aspiring Solicitors, GROW etc). Also, a lot of firms will open applications for their open days in Sept.
5. LPC v SQE: I think a lot of people who are considering self-funding have this question and there is a lot of advice on the SRA website. However, as firms are generally moving towards the SQE I think I would be leaning towards this route. Again, that's probably a reason I would be keen to get a TC first.
