I can think of several contexts in which 'Do you know him?' and 'Do you recognize him?' could be used interchangeably. Even though I recognize the difference, I believe 'know' should be accepted. To 'cognize' is what we do when we make the first 'file' about a person in that computer between our ears. When we see them again, we might think, "I know that person."
I know what you mean: I prefer "-ise" spellings and teach them to my students. OED recognises both forms as standard British English, though, so if "-ize" is good enough for Oxford, we can't grumble too much that the majority of English speakers in the world prefer it. ;)
That it's a yes-no question can be seen by the fact that the verb comes first.
The fact that yes-no questions need "do" is an English thing; German doesn't need it and so "do" is not "implied" in the German sentence -- but has to be supplied when translating into English.