There are a few options you have, but you will need to speak with someone more in depth about your situation.
1. As for your credit score of 554, probably not. But 595, there is a possibility to get you approved, depending on some other factors.
2. There are options for buying a home that do not involve credit checks at all. Again, depending on a few other factors, this could be a viable and legitimate option for purchasing a home.
If you want to find out about your credit, contact Steve Ferguson of Southwest Funding. He can give you some information about your qualifications as well as recommend a credit repair company that won't rip you off. As for no-qual financing, I can help you there.
So to answer your two questions, will disputing things on your credit raise your score? Maybe, but only if you do it right. And can you purchase your first home? Most likely, but you will need a little bit of help from someone who can review your credit, or someone experienced in non-qualifying financing.
I've done several of these types of transactions in the last month, and can give you a heads up about what to expect if you want to chat about it.