In my future computer build I'm planning to have intel-i7 6700k, and on intel's site it says that the memory type it supports is DDR4-1866/2133, does it mean I can only buy ram with 1886/2133 core speed ?
No, that's just the speed it officially supports. Faster memory is considered overclocking, but it works just fine way above 2133.
The CPU is also compatible with DDR3 memory, but officially only at a voltage of 1.35V. Again, higher voltage isn't ruled out, but if it fries the memory controller it's not Intel's responsibility.