First off, how long have you had her? It sounds like you might have to give her a week or two without handling because she seems really stressed out.
Also, what's your setup like? It could be something with her enclosure that is making her stress.
1. Not necessarily. "Exploring" is usually the snake trying to escape, so it means the snake is stressed. In the enclosure the snake shouldn't be "exploring" but should be either in her hides or just laying out, chilling there.
2. Whenever you pick up a snake you want to go for the middle-ish part of the body, not too close to her head because you'll spook her (most snakes are head shy because they have no limbs to protect their head)
3.when was the last time you tried to feed her? Usually with a snake who rejected food because of stress you don't want to offer food too often because that will start to freak them out too (viscious cycle lol). I'd say just wait until its been about five or seven days since the last attempt and don't handle her (unless its taking her out for cage cleaning) until she's eaten for you.