DDR2 and DDR3 RAM have different physical connectors. They cannot be interchanged, unless the board is specially designed to have both types of slots. Even then, you cannot use both types at the same time.
You can put different speeds of the same type of memory in the board, but the faster memory will run at the speed of the slower memory.
not sure this is 100% correct. ddr2 and ddr3 both come in form factor 204pin sodimm (and others).
my hp 100z only has two mem slots and is ddr2 and ddr3 compatible.
with boards that have mem controller that interleaves (most if not all chips today) say 2/4/6 slots it may be possible to run ddr2 in one channel and ddr3 in the other, likely depends on the memory controller. but is it the norm to use the same type and speed ram.