You are asking a lot of different things.
When it comes to income from recordings there is two different types of royalties: royalties for the people that get the credits of writing the song (music, lyricks and/or both) and for musicians that actually play on the recording (wether they get credited or not). Producers are most of the time considered to get a part from the 'writing'-credits, a part btw that is much bigger then the part for the performing musicians on the track.
These royalties mean money every time the recording in question is played on the radio, tv or anywhere else.
What any of these people make on the sales of records is totally dependant on what they agreed on with their record company. The record company gets the income from sales. The artist get's his or her share from the company - if they had a good deal with them of course.
The construction of how company's pay artists has a million different possibilities depending on the contract they have with eachother. Possibility is indeed a share in the sales, other one is that a company offers X-amount of money for the artist to record X-amount of albums, or a combination of the two... etc)
Playing coverversions in a live situation is always free.
Releasing coverversions (wether it is a studio recording or a live recording) is never free. What it costs, if you get permission or not is up to the people that own the rights to the song. (Could be the recordcompany, could be the artist themselves - again depending on their contracts and agreements between eachother).