Yes, borrowers with no credit score are still eligible for mortgages. The process might be more difficult and require alternative documentation, but options exist.
At a local government's land record office. This could be in your town, city or at the county court house. Every community is different of where the documents are recorded.
Yes, you can put 5% down or less and buy a multi-family house using specific loan programs like FHA loans (3.5% down), conventional loans (5% down), or VA loans (0% down for eligible veterans).
VA appraisal typically stay with the borrower and not the house (unlike FHA). The appraisal is typically valid for 180 days or 6 months for the borrower on the house.