Is the statement
If I knew you're coming I wouldn't have come
correct? Should we use
If I had known you're coming, I wouldn't have come
instead? Please consider American-British differences.
What is required here is the Third Conditional, in which the speaker imagines a situation which hasn’t actually happened. In this example, the speaker didn’t know the person addressed was coming, and so, we are led to believe, the speaker came as well. The usual form taken by the Third Conditional is if + past tense of have + past participle of the main verb, followed in the main clause by would have + the past participle of the second main verb. This produces If I had known you were coming, I wouldn't have come. A simpler example is If you had run, you would have caught the train.
The past tense may sometimes occur in the if clause (If I knew you were coming . . .), but in British English, at least, it would be unusual. That said, I expect some of us will know the song that has the line If I knew you were coming, I’d have baked a cake.
A standard way to say this in the US is
If I'd known you were coming, I wouldn't have come.
You cannot contract "you were" to "you're"; this contraction is reserved for "you are". However, "I had" can be contracted to "I'd", and I suspect it usually would be in speech.
If I knew and If I had known in this sentence don't bother me, and I think both are correct.
But I would never use the present tense of be (or come) in this sentence, I'd use the past.
So I'd say either :
Not being a native speaker of English I'm eager to read what the native speakers will write about it.
As far as If I knew and If I had known are concerned the only difference I can think of is that if you're a purist If I knew would only relate to a future event, better give an example:
But still, on that too I am waiting for an expert answer.
You might hear this spoken in the US, but no (decent) grammar teacher would mark it correct on an exam.
If I had known is the standard counterfactual past conditional (meaning, the conditional used to describe something that didn't actually occur).
What about modifying this third conditional to: "Had I known you were coming, I would not have come." What tense is that?
I was taught to keep my writing short and to the point. So my answer would be, "Had I known you were coming, I wouldn't have.