Legal Question in Landlord & Tenant Law in California

The lanldord can request, as part of settlement, that you drop any claims that your may have against her such as your fair housing complaint. This is what is refered to as a "global settlement", meaning that the parties are settling all claims against one another which would include claims not at issue in the current case (your unlawful detainer). It is up to you to decide whether or not what the landlord is offering is enough for you to release your other claims.

As far as the request that you agree to not testify in another action in which you are not a party; that may not be proper. The law is clear that you cannot threaten criminal prosecution to gain an advantage against the same party in a civil matter. I do not know if there is a similiar rule regarding the blocking of a parties testimony in another civil matter. Even if you agred to such a condition I think that you would still have to testify if subpoened by your parents.