Broadcasting House holds far more than it was originally intended to when development started. They couldn't not use all of the space available in the building, whenever I've been there there's barely been a spare desk
Yes - compared to lots of other BBC buildings (PQ and Salford in particular) NBH, Peel Wing and OBH seem to be far more densely populated (OBH maybe slightly better).
In many areas the original desk layouts have been squeezed to fit more people into the same amount of space, and it's common to see people working in communal breakout areas when they can't find a desk. Even with the bulk of BBC Studios moving back to W12 (they are now based in the Broadcast Centre mainly) the building is still very full (as other parts of the BBC have moved in or expanded)
How much staff are based at the Television Centre site? BBC Studios are of course in the old news centre site, and of course there are the three television studios, with TC2 and TC3 probably run by ITV mostly with BBC Studioworks just there to oversee.
BBC Elstree is the main hub for television production I assume, as it seems this is now there permanent headquarters. I have heard the deal between BBC Studioworks and Elstree which ends in 2020 will almost certainly be extended again, another five years I have heard.
Finally broadcasting house is the main admin headquarters, it would be obvious. It is a very cluttered building. Huge amounts of staff have to work there, especially with the vast news centre and news output.
Wogan House is a great help, as it means BBC Radio 2, 6Music, BBC Club and offices are there to ease the load at times.