“Do you hold as true, that the existence of One G-d who created the world and runs it, is proven by logic and irrefutable?”
The answer to this question is an absolute, “NO!”. Any G-d whose existence can be proven by human logic is no G-d, at least not a G-d who is worth worshiping. G-d is far beyond any human power to comprehend.
There is also the problem that if you set out to prove the existence of G-d you admit that it is potentially possible to disprove the existence of G-d. I can’t understand why that would not be heresy.
“Do you think that is a necessary belief?”
Yes, at least for Jews. It is one of the few questions that prospective converts to Judaism must be asked.