Greg Cox speculates that the exile of Khan's group was classified, and as Project Genesis was also classified, you ended up essentially with the right hand not knowing what the left hand had done. This seems reasonably plausible to me.
Chekov not recalling that Khan's group was there is more difficult to explain, but it's not as though I remember every place I might have visited in the past 15 years, and I've gotten around a lot less than Chekov did.
Also, as pointed out above, Chekov wasn't navigator at the time.
As for Khan knowing Chekov, I never had a problem with it.
Given that Khan's group was marooned for years on a planet with, presumably, a different orbit than Earth's, the 15-18 year discrepancy never bothered me either.