None of the options are ideal for the C-Train, though it's not clear where the south stop drops you off - if it's somewhere near to MacLeod Trail, you may be in the neighbourhood of a C-Train station and a longer ride back up north.
More likely, go to the main depot at the edge of downtown. From there you can try the hike back to the C-Train at 7th Ave, between 7th and 8th Street (N. side) which will get you up to the University area (Dalhousie train). It's quite a ways (8 or 9 blocks since you can't go in a straight line) and it's not a great area to walk - the station is kind of on the side of a major artery. Bus station marked here and the area toward downtown.
http://tinyurl.com/yjtzwl
Not sure about buses down there, probably not a great number of options either. There is a 31 that I believe will get you close to that C-Train stop, say within two or three blocks. Double check that one though.
Certainly easier just to cab it from the depot up to the University area - a 10 minute ride max. unless traffic is really bad.
To get to the passport office (and back), the train will work pretty well. Take the southbound Somerset/Bridlewood train to City Hall station. 3 short blocks north on MacLeod Tr. (which is 2 St. E.) gets you close to the Harry Hays building. Reverse it all on the Dalhousie train from Olympic Plaze station (on the opposite side of the street) to get home again.