Erm OK?
1 ATC would only be contacted if the tug wanted to move off the apron ie when crossing an active runway etc
2. The airbridge is operated by the groundcrew/dispatcher. ATC has no input there.
Stand allocations are usually passed to ATC via computer. At London City ATC plan the stands and then tell the ground crew, although this may have changed since I was last there.
If airbridges are available the aircraft taxiing in will taxi down a line and then stop when a lens/light system tells them to. The airbridge is then moved into place.
Hope this helps
CF