Thank you Christian. I will answer your questions below:
1. Is she liable for not keeping my £720 deposit in a deposit scheme?
Yes, because she is the Landlord and therefore are liable.
2. Even though I did not paid her directly the £2400 (which represents all the tenants deposits including mine £720 deposit) but I paid the tenants when they left, wasn't she supposed to keep the money in a deposit scheme?
That does not matter. She was the Landlord at the time
3.Can I claim my rent back for the first 2 months-unlicensedHMO
You can try, but just because it was not licenced does not mean you did not stay there. It would be for the Council to prosecute the Landlord, but I think it may be hard claiming your money back, because there was a contract.
if I really need to pay a solicitor to represent me or if I can carry out the "job" of going to court and representing my self - without a solicitor
If your claim is for £10,000 then it will be a small claim and you dont need representation.
If its a small claim and you pay for a Solicitor, you cant claim these costs back from the other side.
Can I clarify anything for you about this today please?