FHA loans, as well as conventional loans take approximately 30-45 days, depending on how fast the parties involved can meet the conditions of the lender. Most conditions have to do with the borrower providing all documentation requested in a timely manner.
The fastest time for a loan to be approved is about 10 days, and there is no "longest" time. Again, if the conditions are not met promptly, the loan can drag for months and months.
Under an FHA loan, the down payment does not fluctuate, it is always 3.5% unless you are using an FHA loan in conjunction with another program, such as a down payment assistance program.
Closing costs are associated with the purchase price and as a result, will fluctuate. The more expensive the home, the higher the closing costs. There are many fees associated with a closing and most of them will fluctuate. Some of the fees that remain constant regardless of the purchase price are the Notary Doc Signing Fee, the messenger fee, wiring fee, recording fee, and (sometimes) the escrow fee. There are escrow companies that charge a flat fee, and there are others that charge based on the purchase price.
There is nothing to lock in at closing! The only thing that can be locked is the terms of your loan, but this is not done at the closing; it is done prior to closing, when your loan officer feels that rate is at its lowest cost, and that it will move up. The other thing that can be locked is your credit score, but this is a bit more complicated to explain.
You need to understand that the 3.5% down payment, is completely separate from closing costs. The down payment is money that is going to the seller, and this money will reduce the amount of money that you will have to borrow. This 3.5% can also be looked at as equity. The closing costs is money that you have to pay for the different services involved in completing the transaction. There are many services involved. Some of them include 1) escrow, a third party whose function is to bring together all of the services involved and is the heart of actually completing a transaction. Escrow agents follow the instructions given to them by the buyer and the seller. 2) title, a company that will issue a title insurance policy to make sure that you are protected in case any clouts appear on title 3) loan officer, the person responsible for helping you obtain the loan 4) Notary, individual that will make your signatures legal. There are other services that your have to pay for at closing.
Hope it was helpful!
Personal experience in the industry.