Just a link to your own soundcloud, not uploaded there as well?
No, it is the link to the tracks that other people can listen to.
Can I provide a "private youtube link" to the screen recording of my songs, or does it need to be public for all to see?
It should be public (or unlisted on YouTube) so people with the link can still see it. Alternatively, you can just provide screenshots instead, which is allowed.
Hope this helps ^^