As with everything in music - opinions of cover versions are as subjective as they are various.
They range from the sublime - Joe Cocker's With A Little Help From My Friends, to the awesomly horrible - anything by Westlife or Boyzone.
The song writers obtain a varying amount of royalties depending on the small print in their publishing contracts - none-writers of songs in bands receive performance rights only for songs, so nothing from covers.
Approval once again depends on rights ownership.
A good example was Neil Aspinall who oversaw the use of all The Beatles' music for which they owned copyright. He would not sanction the use of Beatles music in any adverts, or allow their inclusion in any compilations.
Since his death in 2008, use of Beatles music in adverts hs commenced, and increases year on year - his successors obviously do not share his sense of purity.
Similar minefields are encountered with the noble art of sampling - a most famous example being The Verve, who sampled a section of the orchestral recording of The Stones' You Can't Always Get What You Want without permission.
Mick and Keef might have let it go, but since the rights were owned by the notoriously litigious Alan Klein, he sued them, and they receive no royalties at all for their biggest hit.