Don't forget, when you sign a purchase agreement in MN, you've committed to make mortgage official application within 5 days of the acceptance of the purchase agreement. If you're not even sure about your loan officer or your loan before you write the purchase agreement, you can't possibly make application that quickly. If you want to pursue that program, why don't you go on the website of people providing the program to see what loan officers they suggest. Those people will most likely be well versed on the terms of the loan and easily be able to determine if you qualify.
As for foreclosures, they just want to know it's going to go through. So, the fewer questionable things you do, the better your chances of getting your offer accepted.
2 - Banks are very tight today on lending and they look over everything with scrutiny. Most of these city programs eventually get approved but the approval process can take time.
3 - The financing terms of your offer include the type of financing and the lender being used. Changing those later is somewhat a bait-and-switch thing, but it depends on the purchase agreement language if you are allowed to make those changes or not. If you write the offer needing this program and don't get it you will often lose your earnest money if you fail to close.
On these aggressively priced properties the bank has a selection of offers to choose from..the most attract offer being cash & the least attractive being more difficult loan scenarios with numerous hurdles. The bank wants a quick sale & doesn't want the deal to fall apart because of a snag in financing.
Your offer is not only competing with others on price but also on the likelihood of it closing...and/or the ease of it closing.