The second guy is telling the first guy to start officially dating the girl. When the first guy says he "scored" the girl, I assume he means he hooked up (had sex) with her. Now she wants to see Iron Man 2 and go shooting, which are seen as "cool" things to do in America. The second guy is telling the first guy that he is lucky to have found such a cool girl and that he should get into a committed, monogamous relationship with her. When people say "lock it down" it means that they have found a great person and should "take them off the market" by dating or marrying that person.

I presume he means get the date. Get a promise from her and make it a certainty that they go out together. This kind of local slang is not known to everyone. We understand it by using our heads. In other words, we're in the same boat as you, bro.

Muzzy means you lack the words to express yourself I think while dizzy means to feel light headed

in this sentence it kind of mean " to do it " or " go for it "