Sunvox,
Some of the items that you are looking for are available on CCS: I have listed a few. I don't know anything about what the instructors can pull up or have access to:
First, I can not access another pilots current schedule or pairing.
I don't know of a way to pull up another pilots schedule, but you can find the pairing information under the "Flight Planning" tab.
Third, bidding individual pairings was easy because a pairing summary was available in 9 pages rather than hundreds.
There are pairing summaries for all CAT's. They are located in the Bid Packages tab, which is below the the Bidding tab.