I have heard rumors that say they will be making a 2nd birth by sleep, but how long is that going to take? If they are still working on Dream Drop Distance, isn't it going to take a while? And with Vanitas gone so are the Unversed right?

They have more than one team to work on Kingdom Hearts games. KH Birth by Sleep, KH 358/2 Days and the original KH Coded was all being created at the same time.

 

Also, BBS Volume 2 has not yet been confirmed to be an actual game and the title Birth by Sleep Volume 2 is probably a tentative name.

We don't know if it's going to be a game(not announced yet) but Nomura has said that he wanted to tell 4 untold stories before KH3. Those are "Roxas' time in the Organization(358/2 days)," "Xehanort's past(BBS)," "The King's absence," and "Riku absence." We've already seen the first two that I've mention. the scenes with Mickey and Riku in BBS FM secret ending show them in places we haven't seen, so it's a high chance it will be a game(unless he thinks of another way to show it).

 

Also, Vanitas is the source of the unversed.

There are three known KH teams. The Main KH team, who is currently working on FF Versus XII, the secondary KH team, who made BBS, and the KH Mobile team, who does... mobile stuff.

Beyond that, there is also H.A.N.D., which is a company Square Enix outsourced the work of the Nintendo DS KH games.