I came to know a gal some months ago on Facebook and started liking her. We shared our contact number and we went on a date twice. She told me she likes me and I replied I like her too. I was in love with her so one day I proposed her. She told me she wants some time to think over that. Actually she is a little picky and choosy.we use to talk late night over phone. I'm puzzled. What should I do . She sometimes don't reply my text and answer my calls. Is she avoiding me. Pliz help.

Don't wait around, if she decides to be with you she will tell you.
The more you wait around the more you could be hurt if it doesn't go as you plan to. Try to enjoy life in the meantime, go out with friends
I've been through this couple of years ago and that wait cost 3years of my life,and still didn't work out. It may not be the same as my situation but it would be best if you don't get too much attached to her before being together.

Let me see you dated twice and asked her to marry you?

Most likely things you are a nut case or worst, most likely scared her for trying to rush marriage from 2 dates.

At least according to customs and practices as done in the US