Yes. It should work since the 600 can be used as a master and a slave flash. And the 430 is a slave. It should be able to go off as long as the 600 is in master mode and your camera has both of the flashes set.
Yes, but only in optical mode, which eliminates the many benefits that Canon introduced with the new radio system. When you try to use the remote control on your television, and someone stands in the way, the signal gets blocked and the remote stops working. This is the same concept with the older optical triggering system that you'll have to rely on for the 430ex-II. If you have two 600EX-RT flashes, they'll use a radio triggering system instead, which can function through objects and even walls.
It will, but only the way 430's receive the signal, which is optically, not via radio transmission. So sort answer is yes, but won't be as reliable as getting another 600 (which is much more expensive).