This page from our help center may help answer your question about how to see submissions: https://help.medium.com/hc/en-us/articles/115004848948-Review-submitted-draft-or-post
Recruiting writers to a new publication takes work... I'd love to hear from other editors about how they've done it, but my suggestions would be to go out into the wilds of Medium, find stories that seem like they'd be a good fit for you publication, and then leave comments on the stories inviting the writer to submit!
It definitely takes time and effort to build up a community of writers, and time to edit quality stories... which is why nominators are compensated!