1) Hello Sachin Desai, I acknowledge your question. Yes, through execution petition you can claim monetary relief for it under section 20 of the Domestic violence Act, for it to be claimed you need to prove that you are an aggrieved person as per section 3 of DV Act. The magistrate has the power to order such an order of monetary relief.
You can also approach to magistrate under section 125 of CrPC too. Whereas for appeal it shall go to the high court if the order is granted by the magistrate court.
I hope I have answered your query, if there is any other query do drop here.
Have a good day.