"Is there going to be another BATMAN film? And if so, when will it be out?
Yes, there will be another film. BATMAN is WB's biggest and most profitable franchise and they are not about to let it die. Look for the next film in the summer of 2002 at the earliest.
UPDATED! WB is now working on two, yes TWO separate Bat-films!

"Who is writing the script and who will direct?"
Officially there is neither; but there have been rumors for both. The only known writer was Mark Protosovich who wrote the Scarecrow-as-the-villian sequel BATMAN TRIUMPHANT. Other rumors have named Paul Dini, Frank Miller, and several unknowns as authors of B5 scripts. Also, Scott Rosenberg has turned in a 71 page YEAR ONE treatment to WB. As far as a director, the only names mentiones have been Joel Schumacher(GASP!) and recently Darren Aronofsky (Pi). Schumacher is the one who originally pitched the YEAR ONE idea to WB. It is unlikely Joel will direct, but he may produce. Aronofsky is said to have been contacted to work on a Y1 project. But recent reports have said the director wants to do an adaption of Frank Miller's THE DARK KNIGHT RETURNS.
UPDATED! Paul Dini and Alan Burnett have officially signed on to write and Boaz Yakin is directing the live-action BATMAN BEYOND. Darren Aronofsky has officially signed on to write and direct BATMAN: YEAR ONE. Frank Miller will co-write the screenplay.

"Will the next movie be a sequel to the last four films?"
No. The next film will be an adaption of Frank Miller's YEAR ONE. Now, BATMAN BEYOND could be a sequel of sorts to the last 4 films.

"If it is not a sequel, then what is it going to be?"
Well, it was going to be a restart with an adaption of Frank Miller's YEAR ONE. There has been word that a live-action version of the popular BATMAN BEYOND has been discussed at WB (which is now confirmed--Jett). A very recent rumor, and and old one too, suggests it could be TDKR. But Y1 is by far the front runner.
UPDATED! We now know that there will be two Bat-films. See above.

"Who will play The Batman?"
Who the hell knows! A variety of names have been thrown out the old rumor-mill. Take it to the bank that it won't be Keaton, Kilmer, or Clooney; the last 3 Batmen. The strongest rumor has Ben Affleck donning the cape and cowl. However, Affleck has gone on record denying any involvement with a Batman picture. WB now seems cool on the idea of casting a "big-time actor" and will go with an unknown. Josh Hartnett fits this bill.

"What is the deal with this BRUCE WAYNE TV series?"
It is a proposed series that would portray a young Bruce Wayne on his way to becoming Batman. Produced by Tollin-Robbins Productions, it is now on "hold," and believed to be shelved.