Patti Smith Group is a strong contender here. I'll go with the album Radio Ethiopia
The REM clue is a strong tie as Smith and Stipe collaborated on each other's projects.
There are 19 discogs entries for Patti Smith Group
Influencing is high but due may have been paid, I think.
Availability is relatively high, I think but there have been recent represses (specifically of Radio Ethiopia).
Drummer is male.
Radio Ethiopa is the 1st album.
She played CBGB in one her first recorded concerts.
She is in the book, Cinderella's Big Score
Again, the controller is a weak link maybe to lyrics in Because the Night?
She was featured in
Vanity Fair
She's been on the cover of a literal pile of magazines (which antagonizes the hasn't gotten their due clue).
Bananarama has professed love for and influence from Patti Smith.
As far as the TV Set clue, well she's been televised numerous times for her performances but she also has acted in a few off the wall things.
See Patti Smith full list of movies and tv shows from their career. Find where to watch Patti Smith's latest movies and tv shows
www.tvguide.com
(again, diluting the not paid dues deal).