If you buy a REO for $45K, it will be difficult to get a mortgage for $75K. You will need to use hard money. The ARV (after repair value) would need to be at least $110K, maybe even more if the lender's in FL have a lower LTV (loan to value) cutoff. Interest rates and points will be painful.
So, if you could find a property worth $120K, and a lender who will do 70% LTV based on ARV, you would be able to borrow $84K. Assume they charge 4 points and 15% interest. Assume about 2% for closing costs. So, after subtracting out the points ($3300) and closing costs ($1500, just rough estimates), and paying the $45K purchase price, you would have about $34K. Typically you will not get this at closing, or will only get a small portion. As you do the work, the lender will give you "draws" of the rehab money.
You will probably need to make monthly interest payments to the lender.
Once you have it fixed up and rented, you can refinance with a permanent loan. Your credit is largely irrelevant, since its your brother who has the income and is qualifying for the loan. DTI is debt to income, which is his total debt payments (the new loan and all his existing ones such as his house, cars, credit cards, student loans, etc.) divided by his gross monthly income. He may or may not be able to include the rental income as part of the income. Just depends on the lender. The DTI limit will also vary by lender. Do the math. If this is 30%, with the new loan, you should be fine. If this is 60%, he won't get a loan.
The lender may also want to see reserves. Fannie Mae's guideline is now six months PITI payments (plus any HOA fees or other fees) for the new loan, plus two months for any other real estate loans. That's for propertys 2-4. Over four you need six months for all properties.
You may need to wait six months or so before you can complete the refinance. You might find a lender who would do 75% of a new value, 70% will be easier. Keep in mind I don't really know your market, so the situation could be better or worse.