What is most reliable site to get the most accurate credit score?
Each reporting agency tabulates scores differently. Auto lenders use one agency while mortgage lenders look at all 3 scores and use the "middle" score for preapproval purposes.

they just want to have the mortgage in the name of the trust only
Depending upon the lender...US Bank requires it to be a irrevocable trust. Typically the title company can move the mortgage into the trust once the closing occurs.

Rate increase effects on closing fees
Fee's charged having nothing to do with interest rates. Most fee's are fixed and a few vary depending upon your loan amount. Playing the rate game can be risky as rates change throughout the day. Make sure you work with a lender that knows what rates are based upon, what economic events cause them to move...