Can somebody arrested at oman airport

I imagine so as transfer of information can go from one country to another.

It is not that simple.  It is possible only when a criminal case has been registered or a warrant has been issued for your arrest.

criminial case of finanacial case in one country particularly dubai or kuwait or saudi ...can share information write

I already answered. And write properly as I can't understand what you are asking.

when a person arrvies at a airport of oman ,,that paritcular person have bank loan in uae or saudi arabia ,,,can that person arrested at airport of oman

Read what I wrote before. I already answered your question. If the bank has filed a case for recovery and it is from the angle of fraud or intentional attempt to do so then yes.  If not, no.

Please read this situation of my friend carefully:
my friend have draw a advance salary of 1300 from UAE dubai islamic bank
and return to india in emergency ,not went to dubai ,,after 9months he went to saudi arabia via abu dhabi airport.........after 2 years he return to india ...now he want to go back to dubai again ........so he asked his case to dubai police through email ...but dubai police asked him to check in dubai police app any financial cases registered on him
..now he want to travel to oman ..there is any problem from police of dubai  when he goto oman airport

If he transits through dubai, maybe. Not if he goes directly to Oman.  And I have NO way of knowing what cases have been filed against him.

THANKS FOR ANSWER