Great question! Generally, you'll want to install a plugin like Yoast that setups the schema for you. And yes, you'll want it on all pages, generally speaking of course. Every situation and business is different. For example if you're a publisher who is posting 40 articles a day, it would help, but that amount of content it won't be as important since that kind of SEO is different.
Schema essentially tells crawlers what your content is about and gives them a structure to help them crawl your site faster. Additionally, it's important if you want to get featured snippets.
Lastly, I wouldn't worry about toxic links, especially from Schema. The name toxic link has more of a negative connoation that it deserves. Depending on your back linking structure and quantity, toxic links won't have too large of an effect on your SEO efforts.
As always, every situation and business is different!