Yes, a 2600 will work fine with a z77 based motherboard.
Yes, you can install ram faster than 1333, but it will not gain you very much.
Read this on ram speed scaling: http://www.anandtech.com/show/4503/sandy-bridge-memory-scaling-choosing-the-best-ddr3
6gb is a strange size.
ram will come in 2, 4, or 8gb sticks.
To get 6gb, you will have a 4gb and a 2gb stick, in which case, the extra 2gb will operate in a slower single channel mode.
Better to get 8gb in a 2 x 4gb kit.