"Monetization" means you allow Youtube to run ads on your video to make them money, and they give you a fraction of a penny for each view. You can choose to do it or not if they make the offer, but to do so, you must abide by their rules. Unless you're getting hundreds of thousands or millions of hits, the payback isn't necessarily worth it.

It has absolutely nothing to do with Vegas Movie Studio and any content to which you have unrestricted license, including but not limited to royalty-free content. Have your attorney go over the EULA and contact Sony if you have any doubts, but that's usually not necessary..

A more common problem is someone else improperly claiming copyright to your royalty-free content on Youtube. This is a popular scam (they really want a "settlement" from you), and can only be dealt with on a case-by-case basis. Sony Media Software will not do this. You do not have rights to use content licensed by Sony music or entertainment divisions.