CBS OWNS the Star Trek film rights. They LICENSED them to Paramount and JJ Abrams. There's nothing for them to buys - they OWN it.
Yes and no. CBS owns Star Trek and contractually licensed the film rights to Paramount. What is in that license agreement is the issue. CBS may not be able to simply revoke Paramount's license unless that agreement is violated by Paramount (like not releasing a new film within a specified period of time).
Sony Picture's relentless rebooting of Spider-Man, for example, was largely to keep the rights from reverting back to Disney (once they gobbled up Marvel) because they knew they would not be able to get them back (that has since changed as Sony and Disney have come to a new understanding) … EVER! 21st Century FOX and Fantastic Four same deal.
So Yes, if CBS let us say, wanted to put Trek's film rights up for bid they may either have to buy them back from Paramount or wait for Paramount to violate the terms or wait for the agreement expire (which it may not necessarily do). Again, it depends on what their license agreement says.