Mark:
Here are some approximate answers.
The line (really a running track and not a spur) that went down Hickory St. was in place and in use through at least 1997 NORTH of Division Street where it terminated at the team track and ramp. The rail lines on Hickory/Hooker SOUTH of Division Street were in place and in use as recently as 1980 but paved over though in place at Division Street by 1985. Almost all evidence of these lines were removed when the City of Chicago rebuilt the streets south of Division Street in 1991.
See the photos of a Soo Line crew working the team track at Division Street on this website-you can see traces of the rails pushing up through the pavement on Division St.
The line on North Branch St. actually connected back to the Hooker/Hickory track just southeast of the current Pickens-Kane building where they terminated at a scrapyard, forming a loop basically around Goose Island. The spur to International Salt was on the other side of the street. The southern tip of Goose Island, east of Halsted St., was reached via a track that crossed Halsted just north of where North Branch St. ends at Halsted though that track was gone by the 1980s.
I have no idea when the drawbridge to Goose Island was last raised but I would guess it was decades ago. The \"Movable Railroad Bridges of Chicago, Pt. I\" article in the March, 2003, issue of Model Railroader magazine goes into detail on the three movable bridges which served these Milwaukee Road lines, including the one leading to Goose Island. There is no mention however of the last date it was actually raised in this article though.
Waste Management for whatever reason discontinued rail service sometime prior to when the City of Chicago rebuilt the streets NORTH of Division Street in 2001. A new street grid was essentially put in place, and only the track down N. Cherry Street was rebuilt and saved along with a new run-around track. If you look carefully you can still see evidence of the former line to Waste Management at the northern tip of Goose Island where a long section of disconnected track pokes up from the mud.
Hopefully the Chicago Terminal Railroad will revive rail service to Waste Management among other customers. There is room on the north end of the island for a transload facility though it is unclear who owns this land.
Tom