Hi OP!
Everything she is doing (and not doing) is illegal. First things first:
Change your locks (keep the existing ones safe though as a PP correctly pointed out that they are her property). You can buy locks for a few pounds from DIY shops like Wickes and B&Q. There are tons of YouTube vids on how to change them. We did ours when we moved in here and it took minutes to swap them (house is owned, but previous owner rented out for years, and supposedly to some bad crowds - plus we were only given one key on completion).
After changing the locks you should contact her (keep a record such as proof of postage - signed for ideally! Email or text message if you don't have another address for her) and state that you expect within 5 working days:
- A signed copy of the contract (in future, keep a copy of what you sign)
- Proof of your deposits being protected. Link to info: Here
Tell her that if you do not receive the above in the time frame given, you will be taking her to court. If it turns out she has not protected your deposit, you can sue her for 3 times the amount.
You should be able to get support from the housing department at your uni, as well as Shelter and the CAB.
I personally would try to find out where she holds her mortgage, and send them a little anonymous letter stating you believe that the mortgage for that property address is probably not the correct type of mortgage.
You see, I have no time whatsoever for rogue landlords. Exterminate the bastards.