Could a Hayabusa motor (1300cc) fit in a Fiat x1/9 without any body/frame modifications, besides motor mounts?

Sorry, but it just wont work. No transaxle on the Hayabusa. Since you are going to make the engine compartment bigger I'd suggest using a V6 and transaxel from a FWD American car. For a good site to learn about your X-19 go to "fiat forum.com"