Does she like me?

[menykats]

I suggest you get off Facebook and call her on the phone and talk to her personally. That is the only way you are going to get a definitive answer to your questions.
She might be "online" on Facebook, but at the time you message her or try to "chat" with her, she could be talking with other posters and be involved in a long comment thread. Some of those comment threads can have MANY posters on it, and everybody is talking back and forth to each other. Or, she could simply be "surfing" other pages on Facebook. In either case, it is unlikely that she is going to interrupt what she is doing and reply to you immediately.
When a person is on Facebook, there is a little icon on the top of their page or on their Newsfeed page that alerts them to the fact that they have received a message from another user. It is stored in their "Messages" file. When she gets around to it, she can go there, open the message, read it, and respond -- if she wants to.