Clock speed = speed that the graphic card or CPU or RAM, etc. is running at. For example, the HD 5850's core speed, which is the graphics processing unit itself, runs at 725MHz. However, the memory on the card runs at 1000MHz.
The GTX 295 is $500 in the U.S., and the Radeon HD 5970 is meant to sell at $600, but it costs around $700.
The GTX 295 uses a bit less power at full load, less than 3W, but the HD 5970 when idling uses around 40W less than the GTX 295.
The maximum resolution of the GTX 295 is 2560 x 1600. The maximum resolution of the HD 5970 is 5760 x 1200 I believe, however, you need to run three displays simultaneously using ATi's Eyefinity technology with a resolution of 1920 x 1200 to support 5760 x 1200. The maximum single monitor resolution though is 2560 x 1600, like the GTX 295.
Two HD 5870 GPUs means that there are two HD 5870 graphic processing units on one card - yes, it does mean there are two GPUs. The GTX 295 is also two GPUs on one card - it is effectively two slightly weaker GTX 275 GPUs on the same graphics card.
As for the last question - the HD 5870 GPU competes with the GTX 295's two GPUs, but the HD 5970 is currently the fastest graphics card, the GTX 480 comes behind, although not too far away.