You've not stated as to in which case have you been declared PO as that would enable us to advice you better. Still, to answer your queries :
1. Quashing of all three i.e. 498a, PO and DV are possible. But assuming that here you are referring to quashing of PO, yes the accused would need to file for quashing of PO, as anticipatory bail is not possible in PO cases, therefore quashing of PO is the only solution.
2. Generally such money is not deposited in the court except in cases where the court orders such an amount to be deposited in certain suits. An MoU is a mutual agreement, and the court is the judicial custodian but has no role to play in accepting and depositing such payments in the court for payout at a later stage. Although since the MoU would now be in the court, so the other party would ideally fulfill their written and signed commitment, but the risk that the opposite party might oppose the quashing would be there as there is no guarantee that they would honor their commitment. But even if they backout, they would not be able to get any money.
3. As already mentioned above, in such cases no money is deposited in the court.
4. As per the general law, quashing of PO is definitely possible before MCD.
5. You would need to provide a Special Power of Attorney to your father authorizing him to file the quashing on your behalf. Your father would need to appear personally in the Mumbai High Court to file the application for quashing of your PO.