Changing the term of your mortgage can help in several ways. First, if you were to refinance your current mortgage from 30 years to 15 years, you will accelerate the rate at which you pay towards principle each month meaning your house will be paid off quicker. Also, you will save an unbelievable amount of money in terms of interest because you would likely be taking 10 to 15 years off the life of your loan. Second, you can also refinance a 15 year mortgage to a 30 year mortgage. It seems like it might not make sense to do this, but if you have an immediate need to free up monthly cash-flow and you don't want to take out a home equity loan, this can work out to your benefit. When you take a 15 year loan and refinance it to 30 years you will have the same balance only the payments can be hundreds of dollars less than the 15 year loan. The only draw back to this is you will pay more in interest over the live of the loan.
If you are planning to stay in your home for several years, then you can save money by paying points for lower interest rates. You pay up front fees to ensure you have lower interest payments over the course of your loan. Remember, this only works if you keep your mortgage for several months.
You have a legal right to a good faith estimate. Get a copy of this document and go over it with a fine tooth comb, it will reveal where there is a real problem.
When lenders offer a "no-cost" loan, they may include a prepayment penalty to discourage you from refinancing within the first few years of the loan. Ask the lender offering a no-cost loan to explain all the fees and penalties before you agree to these terms.