All of what you stated sounds good, but you need to correct the grammar and reorganize some words a bit. Instead of saying these, try the ones beside them.
Where are you from? Better: Are you new to the area? Followup, if she said yes, " Well, I can be a tour guide if you want to explore the city and see the wonderful sights here. Would you be interested in taking a tour sometime?"
Who do you hang with at school? Better: Have you made any friends yet, because I will be your friend?
What kind of stuff do you like? Better: What are your hobbies? Wait for her to respond and depending on what she say, if there is a place the two of you could go, then tell her about that place and invite her to join you.
I like your blog. What stuff do you like? Better and not a repeat question: I found your blog to be interesting, can you show me sometime what you do for fun? Follow up: If she say yes, then ask her, " That is cool, how about we plan something this weekend, will that be okay if I join you?" If she say yes or counters, then ask her for her phone number so that you can call her and discuss the future plans.
Should I invite them to sit with my friends at lunch since they doesn't have a lot? Better: Would you like to come over and have lunch with me and my friends, I can introduce you to some cool people that are good friends and don't worry, they will not take any of your food off your tray? I will make sure of that.
I have given you a little bit of feedback and I think the last question that you want to ask, which is to invite her to your table should be the first question. Once she has accepted your offer, then you can ask the other questions as the conversation flow allows it. Don't sound rehearsed, okay. Just let the conversation flow smoothly and ask her the questions when the opportunity presents itself.
I hope I did not make you upset. I am just trying to help you get the girl that you are interested to talk to you by giving some suggestions that may help.