You are in the worst possible position a single mom could be in. The first thing you need to do is to go after the father of your children. I know that will add another thing to your full plate. Over the last 35 years I have helped a lot of moms collect child support. Sometimes the fathers had to go to jail, Most legal aid offices will help for free.
If your case was dismissed with prejudice, then the lender cannot go after you for anything. When the statute of limitations runs out, (I think it 5 years) you can sue to quite title and be free of all encumbrances on your home.
The landlord has a right of reasonable entry into the property. A property manager inspection before you move out sounds a little unreasonable. When you do move, take pictures of every inch of the property. This is important. Tale A LOT of pictures.
There is a good chance that you will be able to stay in your home until the end of your lease. But the lenders will put up every road block they can find, including ignoring you. You need to file something in the court file with your lease attached. By doing this, the lenders are supposed to notice you on all matters.
The deposits is something else. That is covered by landlord tenant law. He should give it back.
The problem is that he is not working. To get support you would have to go to court and prove he is not working because he will not work. I your situation, that might not be an answer that you can do because of your income. You need to contact your legal legal aid office. In our economy you may find that the Legal Aid is over worked, understaffed and low on money. Talk to them. Do not give up.
In addition to the above answer, the lenders may very well let the tenant stay in the house on a month to month basis. The tenant must cooperate to sell the property. They must move out on very little notice.
When a condo association takes ownership of a unit threw foreclosure, they take it subject to the debt. They do not become liable for the first mortgage. Many HOA's are are taking the units and are renting them out. Some times they "forget" to tell the tenants of the foreclosure.