Moving forward do not make multiple applications but it's fine to inquire of multiple lenders regarding their terms. If you do have a Buyer Broker speak with them immediately and ask for their suggestion as to the best lender to work with. The best advice I can offer you is that if possible work with a credit union if you can as their the most accommodating. under no circumstances should apply for a mortgage with one of the big banks (wells Fargo, BoA, Suntrust etc as their the absolute worst to deal with and even well qualified borrowers are rejected by these banks.
Once you do a full application with a lender you will start having to pay application fees & it should not be necessary to do this with more than one lender.