If the landlord can prove that you paid your rent late, and the lease stipulated a late fee if it wasn't paid in a certain timeframe, yes, you can be charged late fees. A "grace" period is allowed by some landlords but isn't legally required. I believe that if the due date for rent is on a weekend or holiday, you can't be considered late if you don't pay on that date but pay the next day or the following Monday.
The landlord has 21 days to return your security deposit. Any damage you do beyond normal wear and tear can be taken out of the deposit. The landlord needs to provide receipts of the repairs done or proof that he has contacted someone about repairing it.
Below is some material taken from a California attorney's website on breaking leases:
The general rule is that you are responsible for all of the rent for the remainder of the lease period, whether you live there or not.*Some rental agreements look like leases because they say you don't get your security deposit back if you don't stay the full year, but on closer examination, they are just month-to-month agreements with illegal non-refundable security deposit provisions in them. Be sure of what you have.
*** If you have no legally valid reason for breaking the lease, the landlord is still obligated by law to minimize the impact of your breach by trying to re-lease the unit. The legal term is "mitigating damages." For example, you leave in month 4 of a year lease. The landlord tries to re-rent it, and finds someone to pay the same rate starting month 6. You owe the rest of month 4 and all of month 5, but not thereafter. The landlord cannot collect double rents.* In the alternative, the landlord finds someone who will rent your $1000 apartment for $900 starting the day after you leave. You would then owe the $100 difference for the remainder of your lease term.* In contrast, if the landlord does not try to re-rent the unit, and you can show that, the landlord gets nothing from you, because of the failure to mitigate damages.* In between is the gray area, where the landlord makes minimal efforts to re-rent, or rents at a higher rate than you paid. The judge would have to determine whether this was a mitigation of damages.*
*** If you have no legally valid reason to terminate the lease, your best approach is to put the fact of your leaving in writing to the landlord, and keeping a copy, mentioning that your unit will be available for viewing by prospective tenants under Civil Code 1954 [reasonable advance (like 24 hrs) notice, business hours only]. You can also put your own ad in the Recycler or equivalent [freebie ads], and have the prospective tenants call you. Write down their names, work and home numbers, and then forward them on to the landlord as replacements. If the landlord claims they couldn't find anyone, you have a list to contest that, and show their failure to mitigate damages.
*** A legally valid reason to break your lease is not that you've moved out, that your life has changed in some way, that your co-tenant has left, or that you've run out of money.** A legally valid reason for the termination has to do with the unit, itself. If it burns down in a fire, or is yellow-tagged after earthquake damage, obviously the lease ends. However, you can find a legally valid reason for eviction based upon uninhabitable conditions.*
*** Civil Code 1942 authorizes termination of the tenancy [of whatever kind] without notice, upon vacating the unit, where the reason for leaving is uninhabitable conditions. The conditions do not have to be so severe as would entitle you to withhold rent. Rather, they are within the same category [and statute] as repair and deduct remedies. That is, if the condition negatively affects habitability, you can either repair and deduct or just leave.**
*** Most rental units have something wrong with them: missing front door deadbolt locks, missing screens, inadequate trash receptacles, defective electrical outlets, slow drains, etc.. If you have a reason like this, and obviously the worse they are the better the reason is, you can legally terminate the lease, even if coincidentally you got transferred to Chicago.* You do need to have given reasonable advance notice, but that can have been oral. If you had mentioned the defect to the manager last month and it still wasn't fixed, you would want to say that in your letter of termination, so that the record of your reasonable advance notice would be read by the judge.* Uninhabitable conditions which the landlord fails to fix in a reasonable time are legally valid reasons to terminate your lease.* And yes, pictures and witness would be nice, just in case you need to prove it later.
*** Sometimes, the landlord will agree to terminate the lease, but for a price. Watch out for the terms. A decent release clause should say that if you pay one month's rent, they release you entirely from the rest of the lease. Sometimes, however, the management company tells you that you have to pay them some money to be "released", but will still owe them money for the time until they get the place re-rented; you would be paying the "release" money for nothing, since the rest is all you would owe anyway.**Make sure you aren't giving up your deposit, too.* Sometimes they say you're "released" from the lease, or "don't worry about it", and then they hit you with a bill or judgment for the remainder of the lease.* If they are sincere about it, they'll put it in writing.*