Can I install my 9-speed cassette on a 6/7 speed rear wheelset?

No, you can't. Heres why:

1) The spacing on a 9 speed rear is 135mm. A 6/7 is 120 or 124mm. No, you can't "squeeze" the frame to fit;

2) Most 6/7 speed rears are freewheels while ALL 9 speed are cassette. These are not interchangable;

3) Even if you could overcome the above 2 items, 6/7 speed wheels are generally of low quality, and on top of that the axle would be too short among other things like wheel dish, etc.

Yes you can use a 9-speed derailleur on an eight-velocity cassette. All Shimano derailleurs use the same pull ratio, which is 2:1. So pulling an inch of chain moves the derailleur a 1/2 inch. On account that 9-velocity and 8-speed cassettes have one-of-a-kind distances between gears, the shifters for every will pull extraordinary amounts of cable between detents. So the shifters, peculiarly the rear shifter, is the phase that ought to suit the cassette sort.

Both of those are single wall construction. Junk. It needs to specify 8/9 speed hub.

This is more like it. Double wall and a SRAM hub that is compatible with 8/9 SRAM/Shimano

http://www.amazon.com/XLC-Inverno-Rear-MTB-Wheel/d...

Both the wheels you provide links to have freewheel hubs. No way you will ever be able to install ANY cassette with any number of speeds on either of them

A better choice assuming you're cash strapped: http://www.performancebike.com/bikes/Product_10054...

I've put several thousand miles on one of these the last couple years (my old rim disintegrated from hard use), and its performed just fine.

P.S. Bikeworks addressed why your choice wouldn't work, so I left that alone.