I feed my pigs pieces of (green) bell peppers every day. Romaine lettuce, cucumbers, & cilantro are among some of the other vegetables I give them as well. Always do your research if you are unsure if a certain vegetable is safe for a guinea pig to eat. Make sure to not overfeed them either.
Guinea pigs usually have their eyes open while they sleep, which makes it look like they're awake when they're actually not. Guinea pigs do sleep with their eyes closed but they just don't do it often.
A guinea pig can be nervous during their first few days home. Try not to startle or scare her so she can feel more at ease, maybe even leave the room if she refuses to come out while somebody is there. Provide her with a tunnel or two so she can hide. It might take days or weeks before your guinea pig starts trusting you. But remember that if you're patient and gentle with her, you'll be able to form a close bond with your guinea pig.