Hey Gerson congrats on taking action you should be proud of yourself! As far as the hard inquiry goes, I have been told multiple things by different lenders - some say you have you have 45 days and some say you have 14 days. It depends on the model that the lender uses, so it's always recommended to ask your potential lender about how long you have to shop around the loan. Because the last thing that you want is getting a second hard inquiry on your credit report.
Some of the questions I would ask a lender are:
1. What type of mortgage is best for me
2. What is the maximum home price I can afford
3. How much down payment is required (can be 3.5%, 5%, 20% etc)
4. What will be my monthly payment and what is the breakdown of it
5. Am I eligible for any down payment assistance programs that you are aware of
6. What is the estimated APR on the loan (remember that your interest rate on the loan is not the same as the cost of the loan)
7. What is the average loan processing time
8. What fees do you charge
These are some of the important questions that you will want an answer to. And remember that you are the customer, the bank wants your business. So make sure to use that to your advantage. Good luck!