Yes you can. There is no such thing as "dual channel" or "triple channel" memory, only dual or triple channel architecture. Whether or not your system will run in dual or triple channel is up to the motherboard and CPU, not the RAM.
For example, all DDR3 memory modules are capable of running in single, dual, or triple channel. It just depends what situation you put them in.
So in your case, if you put 4 modules (3 from the 12GB kit and 1 from another) on a motherboard with dual channel architecture then it will run in dual channel.
Or you could take the same 12 GB kit and put the 3 modules in a motherboard with triple channel architecture, with a core i7 triple channel cpu, and your system will run in triple channel.
Yes you can, and it will run in dual channel mode.
If possible it is best to use a single kit (one 4 module kit as opposed to two 2 module kits), but it doesn't mean you have to do this. They sell RAM in kits for a reason, but mixing kits is fine as long as the speeds, latency, and timing match. Nothing is 100% when it comes to memory, but if you have 2 identical kits of 3 modules, using 4 should be perfectly fine.