I have 1 domain with 2 subdomains. for example:
Would linking these three domains to each other through the menu, content, and pictures with do-follow links for SEO be useful?
For SEO purposes, the fewer domains and subdomains you have, the better. Subdomains don't really help boost the main domain and if people link to the subdomains rather than the main domain, you're diluting your influence.
It's a little harder to tell what you should do in your particular case without knowing what specific content and audiences you have. You could use the news and video subdomains as CDNs, and that might slightly help SEO by speeding up the main domain. Or, if they are truly separate websites with different audiences and content, you would be better off setting up completely different domains for them and then linking wherever it seems natural - in the middle of an article or page, not in a sitewide header/sidebar/footer. If you can set them up as separate domains, and also host them on a different block so they are recognized as separate domains, and they truly are separate sites, that could possibly help SEO a bit through the cross-linking, but you'd also have to be building backlinks to all 3 sites rather than just 1, which is a much larger effort.