Is it legal for the landlord to take the plumbing issue off my back rent?

I am not sure what you mean by "back rent." But, in California, plumbing is an issue basic to the tenancy of a unit which must be maintained and repaired by the landlord at his expense unless the tenant damages the plumbing.

The landlord can evict you if you are behind on your rent. Since he will offset your repair costs against past due rent, his offer seems reasonable. You're going to have a difficult time finding a new place to live if you have an eviction judgment on your record.

It depends upon the cause of the problem. If your actions are responsible then he is right to hold you finacially accountable. If not, then it is his responsiblity as owner of the building.

You are only responsible for the plumbing issue if you directly caused it. Although, you should keep in mind that he can evict you at any point for the back rent you owe. Read very carefully.

The answer is, it depends. The duty to repair could be in the lease or rental agreement and it would state who is responsible for the repairs. The tenant may be responsible for all repairs or none of the normal repairs. I am making an assumption that the tenant did not cause the plumbing problem due to actions of the tenant by perhaps dropping something in the toilet. The tenant is always responsible if the problem was caused by the negligence of the tenant. Tenant needs to contact an attorney to have the attorney review the lease to determine if the tenant is responsible for normal repairs and maintenance.