What are these tools in this bike maintenance toolkit?
the big wrench below the chain whip

Is for removing the cups on shimano hollowtech II bottom bracket.

http://www.madegood.org/bikes/repair/remove-a-shimano-hollowtech-bottom-bracket/

the thing in the upper right corner

Is for screwing in the preload cap on a shimano hollowtech II bottom bracket.  The preload crap is screwed in to the non drive side crank to keep everything together before the crank is tightened onto the spindle.

http://www.madegood.org/bikes/repair/fit-a-shimano-hollowtech-crankset/

the truncated triangle below the cassette tools

Is a spoke wrench - each of the 3 sides fit a different size of spoke as per the numbers on the corner.  You fit the side over the spoke nipple and the spoke can be tightened/loosened as required.

and the thing next to it.

That's a crank puller for removing cranks from an internal bottom bracket.  There's a cap you unscrew with a hex wrench and then that tool screws into the thread the cap was screwed into.  You then tighten the other end with a spanner which pushes the black bit through and pulls the cranks off.

https://www.parktool.com/blog/repair-help/crank-removal-and-installation-three-piece

Also, the small wrench opposite to the chain tool has a 90 degree protrusion at each end.

This is for removing chain-ring bolts.

http://www.bikeradar.com/gear/article/how-to-change-chainrings-video-42644/