I need help with a girl thing.?

theres this girl at school im starting to really like. and she is sorta new shes only been at our school for a couple of months now. Ive talked to her twice now and she will initiate eye contact and smiles with me and i will do the same. i talk to her when no one else does in the morning time. i just ask basic stuff like how are you doing stuff like that. and i dont know what to do next? and when she looks at me she doesnt look away real fast. even tho the question i ask are kinda yes or no she trys to make her answer longer is that good or bad? And after i started talking to her one of her friends sent me a friends request and she never sent me on in a lil over 10 months thats how long ive had facebook is that just a coicidence or does she know about me? and should i just ask her out to a date after a few more encounters? and how can i deepen the conversation like what questions can i ask to deepen the conversation?