Just wanted to add, my house listed for $85,000. I offered $65,000. The bank said no, I went up to $70,000 with bank paying $2000. towards closing fees. They took it.
Also when I was looking, there was another foreclosure. It listed for $109,000. Realtor gave them feedback that I liked it but was out of my price range, they told realtor that they had just lowered the price to $85,000.
Banks do want to get rid of those foreclosures, they are paying the taxes on those houses.
I wasn't eligible for the grant that you are applying for. I had already owned a home with my ex, so I don't know anything about that.
I also had the money for the 20% down payment, so the mortgage was easy for me to get.
I don't know about getting a mortgage if you need a PMI.