Good afternoon Charlotte,
I'm Doug, and I'm very sorry to hear of your situation. My goal is to provide you with excellent service today. I have been a CA licensed attorney for more than 3 decades.
Rent rates going up are just part of renting in the US lately. As for the date that the payment is due on, most landlords have rent due on the first of the month---whether they have a grace period or not and so your landlord wanting to make the rent due for the month due on the 4th is perfectly acceptable and is no reason for you not to agree to renew your lease for another year.
Unless you are going to refuse to continue to live there because of the rent increase then you should go ahead and sign the new lease agreement.
By the way---the $120 late fee is almost certainly illegal. CA only allows late fees that are approximate of the actual loss suffered by the landlord because they get the rent late. while $25 or $35 is generally acceptable, $120 for a late payment will almost certainly not be approved by the court if you fight it. Ignore the contract and what is says about the $120 late fee and if they r=try to charge you either just don't pay it or sue the landlord to get it back if you pay it.
You may reply back to me using the Reply link and I will be happy to continue to assist you until I am able to address your concerns, to your satisfaction.
I hope that I have been able to fully answer your question. As I am not an employee of JustAnswer, please be so kind as to rate my service to you. That is the only way I am compensated for assisting you. Thank you in advance.
I wish you and yours the best in 2016,