If I sue the homeowner of the house I am trying to buy for breach of contract, can he still sell the house while the lawsuit is being resolved?

Probably not, if you are suing for breach of a contract to sell the house to you.  In most (if not all American) jurisdictions, a plaintiff who has commenced, or will shortly be commencing, an action which affects title to real property can file a "Notice of Pendency" or "lis pendens" (different names depending on which jurisdiction) against the property stating that he/she/it has a claim to ownership.  The lis pendens acts as a lien on the property, and usually effectively preventisi ts sale (theoretically, someone could buy the property, but it would still be subject to the lis pendens, just like if the property was sold without first satisfying a mortgage on it) during the pendency of the litigation.