When searching for a home loan, can I get two or more mortgage brokers to search for the best rate for me and at the end just choose the one that found the best rate?
While it is possible, it's not a really good use of your time or theirs. Mortgage brokers have access to dozens of lenders, can assemble deals you can't even dream of, and are much more intimately acquainted with the latest lending rule changes than you are. They are paid by the lenders to bring them business, so there is no cost to you. A mortgage broker has the advantage of leverage because he can be placing 10 mortgages per day, while you will be placing one, once.
Your mortgage broker is working on your behalf. Get out of his way and let him do his job so you can concentrate on other matters. If your concern is that you want the lowest rate, share that with your broker and let him find the best rate for you. If you want a deal where you can put a larger prepayment down, let him know that and he will find you what you're looking for.