I've been renting a room in California, USA for like 4 years. The rent is $650/month. For the last 10 months, there has been serious noise issues coming from the landlord's household. Those are: loud talkers, kids' screaming, kids' crying, yelling at kids, kid jumping in the bathtub,....that sort of things. It has worsened to a point that's intolerable. Last week, I gave the landlord a complaint letter regarding their noises, and he didn't seem quite happy and willing to fix the issues. Chances are he might turn into hating me, and refuse my rent payment to create a not-paying-rent cause, then file an eviction lawsuit against me. Is that legal? And if that happens, how can I prove to the court that I offered him the monthly payment, but he refused to take it?
This would be pointless and wouldn't work.
Eviction due to defaulting on rent requires the landlord to give 3 business days notice, in writing. This must include a method by which the tenant can settle their debt. Either the landlord would be forced to accept a payment or this would not be valid. Source
Additionally, in this case, there is nothing stopping you physically handing an envelope of cash to the landlord as they live upstairs.
However, there is no reason for your landlord to do this. If your landlord hates you that much it would be far easier for them to simply give you 60 days notice and terminate your tenancy that way.