Can the heroes pick up gems while standing still?
No. Heroes can only pick up gems when they land on them as part of their movement.
Can heroes exchange gems with each other?
No. However, when they are both at a meeting place, they can use gems from either or both of their sacks to pay the gem cost of a troll banishment spell.
Can we choose not to move a hero on our turn?
No. Each player must move one (and only one) of the heroes on their turn using at least one of their movement cards. If the movement cards permit neither hero to move, then the player discards all of their movement cards and ends their turn.
Can we win the game if the dragon has captured a child?
Yes. It does put more pressure on you, and you may need to give rescuing the remaining children a higher priority, but it is certainly still possible to banish all the trolls and win.
Are the starting positions of the heroes fixed?
Yes. Esmeralda starts at her campsite and the Wizard starts in his castle. Note that these are not meeting places, and both heroes will need to be moved at least once in order for players to banish their first troll.