wow, this is a lot for one question...
There are a few methods of redundancy on the CSS.
The first is the most basic and it is box redundancy. The backup CSS in this mode is not used at all and does not send or receive network traffic.
The second is VIP/Interface redundancy. In this mode, it is possible to have one CSS active for all VIPS and the other backup for all, or split some VIPS up on each CSS. Either way, the actual CSS network interfaces are active and forwarding.
Later versions of CSS code also support a method known as Active Session Redundancy (ASR). This method has a link between the CSSs copying the flows, so the backup can take over mid flow if there is a failure. This is also referred to as stateful redundancy.
You may also see a mention of "shared vip" redundancy. That is rarely used, and almost always misunderstood. I recommend not using this method unless specifically told from Cisco that you would benefit from it. Otherwise, you can cause issues with duplicate IPs and other problems.
-Steve