"Come into the light"

I think she just wanted to know what she was getting herself into. She finds a seemingly abandoned castle in the middle of a dark forest, her father locked in a dark prison tower, and locked away by a mysterious jailer who keeps slinking around in the dark where she can't see him.

I think humans (and most creatures) are more afraid and unsure of the unknown than the horror they can really see. That's why many people would rather stick to situations that make them miserable than take a chance on something new ("the devil you know is better than the devil you don't know"), and why blindfolding donkeys makes them docile better than treats or punishments. When they can't see, they don't know where they're going or what they're lashing out at, so they're more calm and complaint.

Anyway, I think Belle had mostly decided to take her father's place, but still needed to know who her jailer was / what her jailer looked like before she made the decision.

I'm not sure there was any significant underlying reason that Belle was consciously aware of. I think it's just human nature; we want to know what we're jumping into before we make the leap.

That's an interesting question. I think that, when the Beast asked Belle to stay in his castle forever in order to save her father, Belle couldn't help but thought for an instant that she would probably end up romantically involved with the mysterious owner of the castle. I'm sure that she understood there was a sexual proposal underlying in Beast's offer. When the Beast moved into the light, she was reasonably shocked and frightened. But she could do nothing else but sacrifice herself for her father. Not that she is shallow and judges people by looks, but if the Beast was handsome or at least looking like a human being, that would make her choice a lot easier. But she wouldn't deny anyway.