Sintaga, you present a delicate problem as this girl is 17 and you are 20. Although this is a small difference which later on wouldn't mean much, right now it is a legal liability. It sounds as though she comes from a very traditional home, where if the parents feel that you are violating their rules and expectations for their daughter, they could possibly seek action against you. Who knows?
If you are of the same culture, (you didn't say) then certainly you must know what is expected of you as a potential partner for someone's daughter. If you don't know what the rules are, then you don't stand a very good chance at this point.
There is no use going on about how difficult or unreasonable any particular foreign culture is, it just is what it is and you can only work with what you have.
If you feel that you must insist in getting to know this particular girl better, then go ahead and try to keep up the friendship through Facebook. At some point, you could just ask her if there is any way that you could see her in person. You may suggest speaking to the parents about it, since she is unlikely to go above their authority. If the parents agree, you may be closely scrutinized to see if you would become a suitable partner, so be prepared for that eventuality.
I say give it a try, but don't set your hopes up too highly. Some cultures are iron clad of what they expect in their children's potential partners, and it wouldn't necessarily have anything to do with you as a person, but more wether you fit the description of what they are seeking. Remember, India is a culture that still practices arranged marriages for their offspring, irregardless of how we see it in the west.
In the long run, if things don't work out, then you could use the experience to tally what qualities you liked in this girl and use it to seek similar attributes in others. With patience and good will, you should have no problems attracting the kind of girl that compliments you for who you are.
Blessings!
So I think it would make sense for you to ping her. I think you're overthinking the whole thing. You should basically just poing her and 'go for it'.
There's no harm in asking :) And if you never ask, you'll never get.
HOG Advisor