hey,
well good for you for not being distracted by CHA. since i am so distracted, maybe i can get it off my chest if i just help out and answer a few questions.
first of all, the first few questions were simply technicalities. abhi could have easily moved to the side of the party (the back, the entrance, whatever). and sam could have seen him going in that direction when she was talking to tanvi.
and as for abhi turning. he could have easily turned b/c he sensed that sam was getting closer or was going to touch him, and he wanted to turn before anything happened. and perhaps when he turned he saw sheekha. OR we just could not have heard sheekha's voice because we were supposed to be enveloped in sam and abhi's world (but mostly sam's). In that state of emotions, she was not paying attention to anything else.
as for abhi ignoring sam. that's easy. anyone would do that if they didn't want to give someone mixed signals or mislead them. abhi knows that sam has feelings for him. and if he knows about his majboori, he knows his place. so he can't just mislead sam. he knows that sam is a little childish, and even a simple gesture or him acting normal could be taken by sam as something else. so he kind of wanted to wean her off before she got even more attached or got the wrong picture. ...of course it didn't work yet. but it was smart of him for doing it. b/c as of yet, technically, neither of them have declared their feelings for each other. so abhi wasn't really cheating her. he can easily say, (as he did when he said "one for all, all for one") that he was doing his duty as a HAWK. notice also that when sam decided to stay with abhi, her language and logic for doing so only revolved around doing so for the HAWK team and as her duty. she never said she was staying back because she loved him. (although we know that both love each other).
as for sheekha and abhi and why he's going to marry her...we don't know anything yet. in fact, i don't even know how ppl know she's veer's daughter (maybe i just wasn't paying attention). but we'll have to wait and see.