1. Given that Grandma Longneck is never that alarmed by Littlefoot's tendency to constantly wander off, I'd say that's probably true. Wandering through the Mysterious Beyond for much of her life, she'd probably see freedom to roam as a natural part of growing up, which would explain why Littlefoot is basically allowed to go where he pleases. Yes, I know Littlefoot
technically always sneaks away, but come on, if Grandma's really that worried about where he is, why doesn't she learn from his escapes and watch more closely? At the very least, she should've dropped that "stay in the Great Valley" Wisdom a lot sooner!

2. Haven't seen enough fan names for her, so I'm skipping this one.
3. That's a very interesting question! On one hand, now that you mention it, it would make sense that Littlefoot's grandma dealt with this kind of child before, given her nonchalant attitude every time Littlefoot takes off. But on the other hand, I don't know if I think Littlefoot's mother would have been likely to stray very far. Considering her discussion with Littlefoot about the different herds keeping to themselves, one can assume that's the way she grew up, which might not have provided a lot of room for adventuring.