Sth in HP1 I dont know for many years

1. maybe he did know Voldemort was there Dumbledore did tell Sev that the dark lord would return so I'm pretty sure he expected it to happen.

2. maybe the harm stopped playing after Quirrell got past him and that's when he bit him.

3. like I said in 1 Dumbledore knew it was only a matter of time before Voldemort would return

4. I can't really give you an answer I haven't read all the books but he did play both sides so he probably lied to her

1) Harry's scar hurt whenever he was near Voldemort and/or when Voldemort was feeling a particularly strong emotion. Voldemort was, in all essence, from where Harry was sitting. (It also hurt when Harry was down by the mirror at the end of the book/movie).
Also, I can't imagine that Voldemort wouldn't have any feelings (let alone weak feelings) about seeing Harry Potter alive and well and in Hogwarts.

2)We don't know that he didn't get bitten. We also don't know that Quirrell actually made it that far -- we just know that Severus did.
If he did make it to Fluffy, the harp that he'd used to make Fluffy sleep had probably stopped playing by the time Severus got there.

3) Voldemort was a very powerful occlumence -- he easily could have his his thoughts from Dumbledore and Severus.
I don't think Dumbledore knew that Voldemort was attached to Quirrell (or that Voldemort was incorporeal), but I think that he suspected Quirrell to be in league with Voldemort.

4) I'm pretty sure he lied. During the first book/movie Severus has a "chat" with Quirrell, intimidating him, and warns him that they will have another little "chat" once he decides "where [his] loyalties lie." It could be interpreted as his loyalty to Dumbledore (since it was Dumbledore protecting the stone and Quirrell taking it would mean stealing from Dumbledore, in a way), but, given that Dumbledore wanted Severus to keep an eye on him, I'm pretty sure he was talking about Voldemort.

1. Harry felt his scar was painful because he was almost "face to face" with Voldemort.

2. Severus was not bitten at that moment, when he followed Quirrell. He was bitten when he placed his own enchantments to protect the stone. He stopped Quirrell during another occasion, in the corridor.

3. Dumbledore was certain that Voldemort would return. Hence all the manners of protection around the stone. Also, He must have sensed the Dark Lord's presence, more or less. Severus may have felt it too, through his Dark Mark. Whether he did or not is not important as anyway, Dumbledore must have warned Severus to be careful and look after Harry more closely.

4. He lied to her, of course ! He was perfectly aware of Quirrell's plans to steal the stone for Voldemort, and for which purpose.