As with the Arabic and Chinese language families, different varieties of Romance languages are similar enough in syntax and vocabulary that speakers can kind of make themselves understood to each other if they speak slowly and choose their words carefully. Same with lots of closely related languages, e.g. German and Dutch. But they're not nearly mutually intelligible to the degree that American English and most varieties of British English are or that Hindi and Urdu are.
Regarding the Spanish/Italian example, the father of a friend of mine was fluent in Spanish, French, and Portuguese. Using an Italian grammar guide and his knowledge of Romance vocabulary from the other three languages, he learned Italian in a single flight from the US to Italy to the point where he was able to conduct business in Italy immediately upon landing.