Is it permissible for a wife to refuse intercourse with her husband if he has not given her mahr, knowing that she got married two months ago in a non-Muslim country and her husband is Muslim and knows that mahr is an obligatory right?

The dower (Mahr) is obligatory for the woman. If it is not agreed upon at the time of the marriage contract, the marriage is still valid, and she is entitled to the dower of her peers (Mahr al-Mithl). If the dower is prompt (not deferred), the woman has the right to refuse to go to her husband until she receives it, because it is a compensation for the usufruct. If part of it is prompt and part is deferred, she has the right to withhold herself until she receives the prompt portion.