I'm just back from this year's PyCon UK. There were quite a few GDS people there, they've attended for several years now in increasing numbers. All good geeks doing good work (and recruiting!).
Nope, go to https://www.civilservicejobs.service.gov.uk/ and put Government Digital Service into the organisation field. We’re currently recruiting developers / senior developers and web ops. No pure front-end developers at the moment though.
Re short term contracts, we hire for two year contracts but it’s not explained well that it’s trivial to extend those. We’re also trying to make roles permanent as well in general.
We do, although that doesn’t go through a central system and is on a team by team basis. If you’re interested get hold of me on Twitter and I’ll see if I can point you in the right direction.