Your very first sentence is simply wrong, I don't know what more there is to say other than that you clearly don't understand what Gödel's results are about (hint: they're called "incompleteness theorems", not "contradiction theorems"). Maybe read a textbook? I could recommend several good ones.
The other sentences basically fall in the category of "not even wrong", i.e. basically nonsensical.
>Nobody has found a contradiction in (first or second order) ZFC in over a hundred years.
Yes, which is exactly why we have guardrails like ZFC in place. We got all sorts of exciting results without them. We of course have to keep adding axioms to ZFC - or replacing them all together - because there is a lot of math out there which is outside it's purview.
