That's odd. There's no need to subscribe normally. Just click on the icon and choose one.

Anyway, it's up to you on other photos. All creative works are covered by copyright at the point of creation. Sometimes creators will make their work available under a creative commons licence for others to freely use - that's where Unsplash comes in. It should be fairly safe, if you assume that the people who uploaded the content owned it (there have been occasions when that's not been the case).

Embedding videos into your Medium stories should be OK because the YouTube licence allows for embedding on other sites and creators can turn that off if they don't want people to embed their videos.

As for what you're using in your own videos, again, it depends on who owns the rights. Some stuff is so old it's in the public domain, which means it's out of copyright. Or the government has released it into the public domain - this can apply to some old musical stuff, too.

Ultimately, you can put what you want on Medium, as the risk is yours alone, I think. Although publications may refuse stories if they are uncomfortable about the image permissions because they could have to share some liability if a case of copyright breach went to court.