hey dude!
First off, i do warn you. Girls that are suddenly all over you... i have my doubts. Just keep it in mind, so you dont fall too hard from the breathtaking heights

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Ok, now lets get down to business.
You ask : how do i act around her? Well, i wouldnt really act if i was you. I would just be myself. Dont become dependent on her. Give her the space she needs. Dont try to play it cool, like you seem to not give a shit.
What do you mean by: do i give her attraction back? like in, acknowledge you are attracted to her? If so, yeah ofcourse. If you play it all cool and uninterested, she will lose interest, which is natural.
the "are you touching my ass"... i dont know mate... it seems pretty close to that F & C crap. i dont like it.
How do you ask her for lunch?.... say: hey, i want to have lunch with you. Lets go. Or, hey, i want to have lunch with you on Friday. I ll pick you up at 12, or whatever. State what you want. You are the leader. Dont ask: would you like to go lunch with me? Would you like a sandwich or a burger? Shall i dress you salad with extra ass-licking? You are a man. Lead. State what you want. She can chose to follow you or to do her own thing.
You tend to let people influence your confidence? Why? Hell, how should we know? Why would you care what other people think? You tell us mate

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How do you mean: replying to an IoI? Give one back ofcourse. How? geesh mate. Give me an example of an IOI you want to reply to? Or perhaps, more in general, how do you show interest in somebody? Talk to her, take her somewhere, touch her, kiss her. Take an interest, without going too far. This is the hardest part: at the correct time, be able to let go, to give space.
hope i helped,
cheers and good luck