"Can Omnikinesis defeat absolutely invincible being?" Logic Manipulation > Nonexistence. Otherwise, not really.
"Can it restore what was erased by Nonexistence?" Logic Manipulation > Meta-Existence. Alpha Reality > Meta-Existence, or just straight up Existence Manipulation > Meta-Existence. Could depend on the raw power of the omnikinetic.
"Can it add any existence?" Logic Manipulation > Meta-Existence, Reality-Warping > Creation, etc.
"Can it create laws so absolute that they absolutely cannot be bypassed by absolutely any means?" Absolute Law Manipulation > Almighty Law Creation, or Reality Warping > Creation > Almighty Law Creation. Maybe even Alpha Reality > Omniarch > Almighty Law Creation. This one was a bit tricky though; the omnikinetic might struggle a bit with doing this.
"Can it beat user of Complete Arsenal, after all?" Well, there are some stuff an omnikinetic could do to grant themselves Complete Arsenal as well. Logic Manipulation > Complete Arsenal. Meta-Power Manipulation > Meta-Ability Creation > Complete Arsenal. Reality Warping > Self-Power Bestowal, etc etc. So the omnikinetic could bestow powers to themselves to give themself a better fighting chance. Whoever wins though would probably overall depend on who has more raw power.
This was fun to write, haha. I'm not saying omni-manipulation is Utilifery though, just decided I'd try to figure out a way for an omnikinetic to do the stuff you did just for fun. I agree with you on the fact that there are some stuff an omnikinetic would either not be able to do or they'd have a very hard time with doing.