Well, before you fire, be sure you understand the contractual agreement you made with the property manager. If you don't have an agreement, then go ahead and find a property manager that does (most do, and would be foolish not to). If you do have a contract, then it probably says when the payments are supposed to be made to you. If it just says something like, "monthly" or "each month," then when you signed the agreement, you gave them permission to keep the money for a whole month. If you want it sooner, then ask if they will agree to that and sign a new agreement. If they won't, then find another property manager who will (most will, and would be foolish not to), but don't expect anyone to send you payment any earlier than one or two weeks after rents are collected. If they did, then you run the risk of receiving a check which may not be honored, because the funds haven't cleared, yet. That is not a happy place for anyone to be in.
The laws may be different, so it really depends upon which state (and sometimes county or city) the property is located. However, generally a landlord is responsible for overall maintenance that is not stated in the lease or rental agreement as being your responsibility. Regardless, you have the responsibility to notify the landlord of any maintenance issues that are in need of repair. It's best to do this in writing and include a demand that the repair must be made in a timely fashion, or you will be forced to hire a contractor to do the work and deduct the cost from your normal rent payment. Since there are several items you mentioned as needing repair, be sure to list all of them in your letter, keep a copy and send the original via Registered US Mail, with a requirement for the addressee's signature as confirmation of delivery. When the signed confirmation is returned to you, attach it to your copy of the letter and keep it in a file with your lease or rental agreement, along with any additional correspondence and any estimates and receipts for services you pay for, whether you deduct their cost from your rent, or not. If the carpet was damaged by the toilet overflow in 2010, then the insurance company (not the landlord) would have been responsible for paying for replacement of the damaged carpet. Hopefully you still have copies of the receipts for the replacement flooring, and if so, make a copy and keep it in the file discussed above. Was it the landlord refusing to pay for replacement, or was it the insurance company not wanting to pay? If you're not sure, you need to find out. If it was your landlord's desire to not replace the carpet with hard flooring, then you may be responsible for either covering or replacing it with carpet acceptable to your landlord, but you should still be reimbursed for the amount you spent, up to the amount paid by insurance. If the toilet overflow damage was covered by your renter's insurance policy, then you need to bring a copy of the receipts and talk with your insurance agent about what happened and your re-payment for replacing the carpet. If it was covered by your landlord's policy, then send a separate letter to your landlord (in the same manner as described above), along with a copy of the receipt, requesting repayment from the proceeds of the insurance payment your landlord received.