you do not need to have money saved up for a pre-approval letter, but you will have to have the funds required by the time of closing and you will have to document the source of that income. if you go FHA you can have a 100% gift of funds for downpayment from a family member, and you can negotiate for the seller to pay closing costs. if you find a home in the USDA area then you can get 0% down financing if you qualify.
Unless you go with MSHDA, then you could represent how much money you plan to put down and could get a preapproval letter. However if you make an offer that gets accepted, then you would need to show the downpayment money for formal application or demonstrate you will have it by closing.
No; and if you haven't been a homeowner in the last three years you could be eligible for a $3000-$5000 grant through the MSHDA. Your lender can provide an application for that when you're ready to buy.
Let me know if you need lender recommendations- some are better and faster than others. This link will provide some details about that grant:
You need to speak with a lender. There will be cost associated with a loan, but there are also different loan options that may allow you to roll the cost into the loan. A lender will be able to explain the options that are available to you based on your financial situation.