No, you can't get sued for that. For example, Sony Music may ask you to block or delete the song. If you will refuse, they probably will go to court with an "empty" case. But that scenario is barely possible until you get like 500k+ downloads.
You can learn more with a life situation that Russian network met and how they handled it after
Probably not, because you should be in a position to rely on the Safe Harbor provision of the DMCA.
Safe Harbor protects service providers who provide open, non-moderated spaces for users to directly contribute content. Safe Harbor means you do not need an army of moderators to inspect every message posted to the site or system. It is essential for sites ...
The law recently changed this way less than 2 years ago, so there may be some disconnect between the law and opinions about older law. I would recommend reading the notes section to the statute. Para (c)(1)(B) informs the applicant that
the royalty shall be the royalty prescribed under
subparagraphs (D) through (F), paragraph (2)(A), and ...
When something is subject to a compulsory licensing requirement, as covers of songs are under U.S. copyright law, then you have to options to use it legally:
Negotiate a deal with the copyright holder.
Pay the administratively determined compulsory license amount. I believe that the compulsory license amount administratively determined can include a ...