Triple-Channel and Dual-Channel or whatever will NOT boost performance in real-life applications such as Photoshop, games, Microsoft Word, etc.
But, if you're playing benchmarking software, it helps. Benchmarking softwares are meant for PC Enthusiasts, Extreme OCer(which want to win some titles, etc).

It won't affect performance if you throw in some random RAMs into your current setup.
But, it's not worth to do so. 2GB RAM mixed with 4GB RAM and 2000MHz mixed with other MHz, different CLs, etc. LOL.

For a PC Enthusiasts or OCer, setting up random RAMs is definitely WRONG. LOL.

For normal people, it's OK.

Yes, you can insert the extra memory. Though you will need to observe some caveats (as mentioned below)...

If you add slower RAMs (lower clock speed and/or higher latency), then all the memory modules will run at the speed of th slower memory modules. Also beware that you're using performance memory which has a higher operating memory voltage. For compatibility between banks of memory, usually its recommended for all the memory modules to have same operating voltage. Thus preferably get memory modules with similar characteristics (speed, latency and operating voltage). Otherwise you may need to remove your current performance memory if adding new memory modules causes problems.

your current 2000Mhz rated RAM will downclock to match your HyperX kits. Unless you OC all of them to around 2000Mhz.
I think compability issues should be okay.

Then your memory clock speed will reduced to run at 1600MHz only. Do those have the same operating voltage as your current DDR3-2000 memory modules? Have you checked what's your memory module's operating voltage?

Nope, should be compatible. The caveat is just that the kits wih 1.5V will be running a bit hotter than specifications (due to higher memory voltage). It would be incompatible however if the BIOS defaults to 1.5V memory voltage (which will affect the higher speed DDR3-2000 memory modules), and if that happens then you will have to manually set the memory voltage (to a higher one).