"On" is one of those words that have quite a lot of meanings, plus it is used in lots of phrases with various meanings. The meaning of on, in the term used is this (from yourdictionary):
adjective
arranged or planned for: tomorrow's game is still on
also read through all of the meanings here to try to get the feeling for the patterns.
Now, as to why "You" instead of "I" - well, usually the phrase is used to answer a challenge, and in this case it is more natural to say "You are on" because it is the challenge that has conditions that needs to be activated, accepted or started (there is some semantical overlap between the word "on" and these verbs). Also, you could have several challenges at the same time from several people - saying "I am on" would be ambiguous in that scenario, where "You are on" is not.
A lot of Yiddish words crossed over into the English language in English speaking cities with sizeable Jewish communities. London is probably the best example, and as a result, cockney Londoners use lots of Yiddish words.
As well as kosher, there's chutzpah, klutz, nosh, schlep, schmooze, schtich and others.
As with other cross-pollination of languages, the words that caught on are ones that are shorter or catchier than the existing alternative, or words that have no satisfactory alternative.
None of the alternatives you suggested have quite the connotations that kosher has (or, more importantly, the connotations of something not being kosher!)
The word would have evolved from being a novel metaphor, through to being a commonly used metaphor, to gaining the commonly understood meaning it has today.
By metaphor, I mean that someone would have said something like "I've been offered a job; I'm pretty sure it's not totally kosher". The listener would know what kosher meant in sense of Jewish food preparation, but was able to understand it as a metaphor.
I don't think we're going to be able to pinpoint the moment it passed from being a metaphor to a straightforward word -- it's a continuum. The moment the metaphor was coined is surely lost in history too; since it probably happened in an East End pub in the early 19th century.
Best Answer
It's called pleonasm.
Sometimes figures of speech like this one are used to achieve some particular effect, in this case it's just an idiom being used by imitation, or habit.