I am an owner of three rentals, and the way I manage my properties is that any outstanding balances are settled out of the security deposit, and I remember when my wife returned the keys and house we had to pay for a broken screen or something.

Of course, you will have college student tenants presumably, so get big deposits/cosigners and/or be an amazingly good judge of character!

This person wants to move in with only partial rent upfront.Since they are a roommate, can I do a weekly lease, accept deposit and weekly rent, and give them 7 days notice to leave if they don't pay?

In California you generally have I think 2 or 3 days to make the earnest money deposit.

I would end their lease and do background checks on new potential tenants.Should I still keep security deposit for ending lease early?

I only saw the paperwork I sent to the owner, and the deposits of course.

I did inform the tenant I would let her out of the lease but she want to be compensated with 2 months free rent, security deposit back, moving expenses, and time off work.

That is why I take 1 1/2 times the rent as a security deposit.

Tenants make deposit to BoA with slips that get time stamped.

Even if you dont want to do it yourself you have property managers that would only take 10% or only have of the deposits instead of 100%.