The correct wording is "This is my first visit TO the USA", or "Is this your first visit to the USA?"
If you are going somewhere, you make a "visit to" that place.
A "visit of" means that the object is visiting you. That is, if you said, "This is the first visit of Uncle Joe", you would mean that Uncle Joe is visiting someone.
I may apply general logic here:
semifinal -not fully final;
semisolid -not fully solid;
semi first-name -not a full first name
I'm not an American so exactly don't know how to shorten names. But let me try...
For instance, your friend's name is Rachel Fishman.
Now here...
Fishman: Last Name
Rachel: First name
Rach: Semi-first name.
Said that, if you are close to Rachel, you don't bother uttering the whole name. What I just said up there...
Hey Rach, bring me beer!
So, if Rachel says, "Let me introduce myself on a semi-first-name basis", I think Rachel is trying to be friendly with the audience/opposite person. Said that, on the very first meeting, Rachel wants to be an amicable person and does not want to get into formalities.
Something like...
Hey, that's okay, call me Rach!
Immediately, the opposite person gets feeling of friendliness.
[In your case, as I said earlier, I'm not sure how to shorten the word 'John' further!]
This is a logical answer, and I'm not sure whether it has something to do with 'culture'. Depending upon comments, I shall improve/delete this. Here, I just tried to help the OP.
Best Answer
All generally mean
Either of your questions may be asked
if you're wondering if the listener has ever been to Sydney before.