I believe that Dan Curtis' estate owns the rights to the original series and characters, and probably also the 1991 revival series. MPI holds the rights for home video release of the original series. Warner owns the rights to the movies, at least as far as distribution goes; I'd bet it's quite possible that the DC estate might own the actual IP (that is, someone wanting to do a remake would probably have to go through DC and not Warner).
And yes, absolutely rentals have to be paid to one entity or another for showing the series or movies in theaters, broadcast, or streaming. None of it is in public domain, or will be for a long time. That's why DS can be hard to find on TV--the networks or stations need to make the necessary agreements and payments to the distributors.
A series like the original DS can be a difficult one to market, because it's a continuing series that lasts almost 5 years, and does not at all lend itself to occasional viewing--you need to see the episodes in sequence, ideally not missing any, during the major story arcs. It's much easier to program series in which each episode is a more-or-less standalone story. Furthermore, if a network shows the pre-Barnabas episodes, they risk alienating viewers who cannot relate to them as being DS (because those poor unfortunate souls have been led to believe the show was always and only about vampires and witches and such).
