بسم الله الرحمن الرحيم
(1) It is necessary to pay mahr whatever is fixed. In the question mentioned it should be investigated whether only 32 gram gold or amount equal to it was paid in mahr, then you should pay the rest amount. However if you inform your wife about it then it is better.
(2) Yes, you may touch her.
(3) Whatsoever you did so far it was halal. The receipt of mahr is not mandatory to have sexual relation with wife after nikah, it is alright to pay the mahr later but it should be paid as soon as possible.
Allah knows Best!
Darul Uloom Deoband