Questions:
1.Is habeas corpus applicable for this case?
HCP is not maintainable in this case.
You can lodge a complaint with the police stating that you both are lovers and her parents have illegally confined her against her will by another individual in such a manner as to violate the confined individual's right to be free from restraint of movement in order to prevent her marrying you since you belong to low caste.
This complaint may be escalated to the higher police officer and also it my be spread across on social media and press media to attract others attention for getting a solution to this.
2.What will be time period for the action after habeas corpus petition?
Haebus corpus petition may not be maintainable in this case,
3.What if her parents fail to produce her in the court after filing the habeas corpus petition?
If the court asses an order then they have to produce hr before court, but please note that HCP is not maintainable in this situation.
4.What can i do to get back her and marry her?
Read the first answer above.