So, did Bethesda get the rights to make the single player for just Fallout 3? Or for the entire franchise (meaning, they could continue making Fallout games as long as they wanted)?

After the settlement with Interplay the fallout series is entirely their. Or so I heard...

It would be awesome to see a Fallout 4 or even 5 from Bethesda. They're the perfect company to take up the Fallout franchise since the previous Fallout games and The Elder Scrolls actually have a lot in common. Two amazing franchises are always better than one

Well thats what the DLC are all about, to continue the storyline. I'm sure there will be Fallout 4 or 5 but of course they will probably do Elder scroll 5 before doing Fallout 4.

Bethesda own the Fallout world, and all related IP
Interplay have limited rights to develop a MMO (based on fundrasing and development milestones)
Interplay also have a limited right to sell the old games.

If this game was any indication of the half-assed ness they would put into a possibly Fo4 or 5 I hope they sell the rights.