If you need the 16 GB, I would recommend getting a duplicate pair of either kit, and then using those two kits, as opposed to mixing the 1333 and 1600 kits. However, if you don't need the 16 GB, then yes, I'd recommend using the 1600 kit alone.
Yes, you can; however, it is not advisable. Mixing RAM will often result in less favorable experiences. Further, the RAM that can reach 1600 will have to stay at 1333, because the 1333 kit cannot run any faster.
Problems you may encounter by mixing RAM:
1. BSOD
2. Incorrect RAM operation
3. System may hang or lag
Would you suggest uninstalling the 1333 8 gigs I currently have and replace them with 8 gigs at 1600? I've heard there's only a 1-3% increase in efficiency when jumping to 1600...
If you need the 16 GB, I would recommend getting a duplicate pair of either kit, and then using those two kits, as opposed to mixing the 1333 and 1600 kits. However, if you don't need the 16 GB, then yes, I'd recommend using the 1600 kit alone.