The letter concludes by saying I have a chance to "remediate the problem" by calling or emailing some local government guy. 

What are some of the remedies to this?

I don't know what the remedial actions required should there be found that lead-based paint is in the home.  

NOTICE IS HERBY GIVEN that because of the above dwelling’s condition and chosen remedy, substantially endangers the health and safety of the tenants and your failure to comply with your implied warranty of habitability by refusing to repair defects on the premises, in a proper and professional manger, as previously demanded of you, the undersigned tenant has elected to vacate the premises without penalty in accordance with California law.

An agreement to accept this money negating any potential interest owed would more than likely remedy that issue should any court ask about it.

You will either remediate now or later anyway.

This is something that can only be answered by an asbestos removal/remediation contractor.

After doing this, you should spray the entire unit with either Hit Cockroach Spray or Herbal Strategy whichever you prefer.

Fix the flashing, remediate the mold, replace the stucco and you're good to go.

Was there mold and if so was it properly re-mediated?