How do you shop for mortgage?

[Andrew L.]

As the title implies, I am new to real estate and just last week, I called out a couple of mortgage brokers to see what kind of mortgage and rate I could qualify for. I wanted to do this without incurring a credit pull since I haven't decided whether this is a good time to buy a house (residential, for myself...not looking to make a profit or make it into a rental property). Anyway, so one of the brokers will be starting out with a new bank next week and was kind enough to tell me as much details without incurring a credit pull. Another broker (not sure whether he works for any particular bank) simply asked to provide all the info and he will give me a pre-approval letter. 

I am sensitive to having multiple credit pulls even though my FICO is right around 800, but still I want to be able to compare rates from different sources/brokers. So below are some of my questions:

1) Will a broker working for one particular bank be at a disadvantage compared to one who can pull loan offer from multiple sources? 

2) Can the rate change between pre-approval letter and actually buying a house? Or does a broker has to offer the rate on pre-approval letter?

3) Any tip to shop around for best rate without incurring too many credit pull. 

Thanks!