Preapproval can get done as quickly as one day or may take up to a week depending on how long it takes to receive your required information. 

People are approved up to a certain monthly payment amount: Having to back into that amount by taking into consideration monthly insurance, taxes, etc. Then we also back into purchase price based on down payment.  It is always more important to find out what your ideal maximum monthly payment comfortable level is versus your maximum monthly payment qualification amount. 

The closing costs are mostly fixed costs associated with getting the loan. In addition, there are some variable items to set up escrow to pay for taxes and insurance at closing. Also, potential points to buy down a better interest rate or lender credit for a higher rate.  General rule of thumb of 3% of the purchase price can be a good gauge for homes in the $275K to $375K range. 

Inspections will have to be paid at the time of the inspection. Earnest money is usually paid at the time that your offer is accepted. Sometimes appraisals are paid at the time of the appraisal (other times it will be collected at closing). The remaining items are paid at closing.

Typically, 30-60 days from closing.  Due on the 1st of each month with a 15 day grace period.