1. No marriage can survive without the mutual consent of spouses. So whether your marriage is valid or not you can save this marriage unless you win your wife back.
2. This marriage is though invalid unless at the time of vedic marriage your wife was converted to Hinduism from her Muslim religion which is does not appear to be so.
3. If any of the spouses or live in partner for no reason walks away from marriage no legal action can be taken against him.
4. If she alleges of rape then FIR would be registered against you and unless you take anticipatory bail you may get arrested.
5. Try to cajole her and shower her with love and affection to get her back.
Sadly no case of rape will lie against her nor any case for cheating unless she indeed cheated you and extorted money from you.