What are Queen’s Orders for

It seems to be something related to co-op gaming.

From Destiny Wiki:

Orbs of Light are glowing balls of energy generated by other Guardians when they use their super abilities. Orbs can be picked up by any other player in the Fireteam, and provide a large boost to a player's super ability recharge meter.1 The super ability recharge boost when the player picks up an Orb appears to be larger than the boost that players receive from kills, time, or other actions. Orbs of Light do not appear to serve any other function, and are a cooperative gameplay mechanic designed to encourage players to play in Fireteams and reward them for working together.

Golden Chests just contain loot, yes. It's also worth noting that they scale on the area, not your level. So it's best to find them asap. You also are given an item for finding all the golden chests on a single planet. I know that you get a Sparrow from Earth and an Emblem from the Moon.

There's a few on each of the planets in-game at the moment. There are 5 on the moon

1 - Found during the The World’s Grave mission inside the cave full of cocoons.

2 - Head to the mission marker located in the large yellow building. Proceed until you find the green gas pit. Look nearby for a rock formation and orange lights.

3 - Another in The World’s Grave. When defending your Ghost search a nearby room with a little pool of water

4 - Inside the Temple of Crota during the Chamber of Night mission.

5 - The Summoning Pits Strike mission. After the final boss fight walk to the edge of the room and drop down onto a small platform

I'm affiliated with Gamers Heroes and we have a guide on the topic should you need more direction: Destiny Gold Chests Moon