The information you have provided makes it difficult to answer this question appropriately. For instance, what do you consider a 'fair' credit score? It also sounds to me like your credit score is going to be affected if you owe money to someone and you aren't paying it back, 'mortgage fraud' or not, you apparently signed for a loan and received money for a home and that's about all I can tell from your question. It sounds to me like you need to get busy and get your problems with the mortgage fraud taken care of, but of course, you do need a place to live.
This is a question that I think only you can answer by seeing if you can meet the qualifications of this landlord. Do you have the money that is required to put down on this home in order to lease it? What is your history in renting from other landlords? Have you worked at your job for a very long time? Do you have any other good personal references or work references? Is the monthly rental amount something that you can afford on your current salary? These are the things that landlords look at when making a decision to rent to a prospective tenant. Any area that you might have a problem meeting the rental criteria is something that you will need to work on to correct. You could even ask the landlord what you can do to improve your credit-worthiness, if you are denied your application to rent this house. Information is totally empowering.
Good luck to you in your future.