Couple things, unless your taking about a second mortgage, the Fed rate is not what dictates a mortgage rate. Mortgage rates are tied to the bond market. And while this market is effected by what the Federal Reserve does to rates, it does not dictate what the rate will be.
The best way to get the best rate is to know where rates are on the day your looking, and where they have been during the last few weeks. (Mortgage rates can change during the day because they are tied to the bond market, so if there is a change in this market, a true wholesale mortgage rate will change) You need to know this information if you truly want to get the best rates. This is because most lenders build in a point or so, just in case the rate goes up from the time they quote it to you, and when you call back and lock it. This may sound like that bank is doing you a favor, but in reality they will just make more on the yield if rates don't go up. On the other hand if rates drop during this time, the bank/ broker makes out making more yield.
All that to say research, know what the averages are in your area, remember an average means that some paid less. but at the very least you don't want to pay more.
Both of these do not make loans, but keep averages for the nation right on the home page. And both allow for research.
Fees: most fees are real, if your dealing with someone that has a good reputation, just ask what it is, and if you can see an invoice for the charge. RESPA says a lender cannot charge more than "cost" on 3rd party items, this includes credit, appraisals, title fees, even underwriting and processing. The fees that are bogus are application fee, lock fees and more than 1% origination fees (expect to pay this if your truly getting the best rate) Remember to compare APR as well as rate, this includes the fees, and is on the Truth In Lending disclosure a reputable lender will not have a problem going over this form, someone trying to hide fees will discourage you from looking to closely at this disclosure.