Can you get a mortgage based on SSI? If it is expected to last for a very long time yes. If temporary no.
Can you buy a house with bad credit? 620 or higher yes, less than that you need to find a lender who also works with credit repair. You could not buy now. But in a few weeks, months, or years when your credit is good again you could buy. Depending on what is wrong you may be able to raise your score quickly, or not.
A real loan will require 3.5% down for fha higher with other loans. However, V.A. loans and usda loans are 0% down.
You have faith that going to school will pay you well later on. Use the same kind of faith to cut your expenses, spend less money, and save a down payment for the future. You might be surprised how much removing many things like a cup of coffee a few times a day at the cafeteria can add up in cash savings.
You might find owner financing, but then what happens when you need to buy a furnace for the house? What happens when the roof leaks and you have to replace it? Until you have some money saved you are not ready to buy and keep a house. You lack the ability to keep it if anything goes wrong, and it usually will.