Lease Breach

[piloteng]

What is the name of your state (only U.S. law)? CALIFORNIA

we paid the security deposit and first month rent and moved into the apartment. After 2 days, the landlord brought the lease to sign and we noticed the cockroaches and shower problem as described below. As she forced us to sign the lease or to leave that same night but since we had already vacated our previous place and had no where to go we signed the 1 year lease and added provisions on the lease that a cockroach problem and a shower that is not working be addressed for this lease to become valid. We were never given a copy of the lease to this day. (been 1 month now)

1. 1

The shower was never fixed, it does not mix hot and cold water in the right ratio(taking a shower is a struggle if not impossible altogether). I called an independent contractor(Plumbing company), they inspected and gave me a 900$ estimate to fix it(Will this be enough to contradict their assertions that nothing is wrong with the shower). I can't take showers before I go to work every day. I visited a doctor and was diagnosed with Gastroenteritis .

1. 2

The cockroach problem persisted even after they fumigated the apartment twice, in fact it grew larger in scale (Mainly kitchen and bathroom). We have daily photos of cockroaches in the apartment.
We gave the landlord a 30 day notice to move verbally and in writing. We are leaving on the 12th of August.
We paid 12 days rent and we were sent a notice to either pay the rent in full or quit (They are demanding full month rent and said they will hold me liable for the apartment until it is rented out). Seems they will file an eviction notice soon. What should I do, I am so worried and any legal advice would be greatly appreciated.
I am poor and cannot afford to lose a deposit. I was wondering too if I can get not only the security deposit, but also the moving costs which could have been avoided, the inconvenience this caused (Stress) and the depreciative value of the apartment.

thanks