I don't have the rules in front of me but I recall the answers to your questions are there.
1. Can you move less than the card says? Card says move 3, but player wants to move only 2.It's up to 3. Thus, you can move only 2.
2. End of the game, all cards are used in matches. One wild card is left over. Does it count as a gem?No, a wild card cannot mimic any card type by itself. But imagine you have 4 gems and 1 wild. You can use 3 gems and 1 wild as a set of 4 gems and then another set of 1 single gem. So it's not really a problem in most cases. In some cases, like e.g. when you have 2 trees, 5 carrots and 4 anvils (each set needs 2 more symbols to score an additional point), the wildcard is worth nothing.
3. What is a singleton wild card worth?As above.
4. Does a player, upon reaching the 5VP point of collecting sets, start over with a new set? If a player has five gems, does he score six points?Yes and if you have 8 gems, you get 10 points (5 for each set of 4 gems).