Making a New lease with additional conditions on a month to month tenancy

[Banu Sho]

My tenant is on a month-to-month lease for a long time in a rent-controlled property in LA County. The last lease was signed a few years ago. 

1) If I want to make a new lease adding some new terms to the lease, do I need to give him a 60-day notice of my intention to make a new lease or can I just send him a new lease?

2) Can I raise rent in the new lease or do I have to wait till Jan 31, 2024, to raise the rent because my property is under rent stabilization?

3) If I can not raise the rent now, can I make a note in the new lease that as of Feb 1, 2024, there will be higher rent with 8.8% increase?

4) When I send the new lease to the tenant, is there any protocol on how I should give it to him for signature?