Hey I played the game and read the rules but still have some unanswered questions.

1)

When you receive dragon runes, can you place them in your home realm?

2)

What happens if one player starts a duel with a routed hero?

3)

Can a hero only start duels and attempt to complete quests in the quest phase, or can he also do those things by using the orders cards (1, 2, 3) ?

1) Yes

2) Routed heroes can still defend themselves, so the duel would take place normally.

3) They can only do those things in de quest phase.

1) When you receive dragon runes, can you place them in your home realm?

Yes, as long as you have room. The rule about only having one rune per hex still applies, but if you have Home Realm hexes with no runes in them, you can absolutely put runes there.

2) What happens if one player starts a duel with a routed hero?

Duels are not battles, so nothing special happens if one hero is routed. The duel proceeds normally.

3) Can a hero only start duels and attempt to complete quests in the quest phase, or can he also do those things by using the orders cards (1, 2, 3) ?

Only in the Quest Phase. The order cards that allow heroes to move specifically provide movement, not "a hero turn."

It may be worth pointing out, also, that you only reveal Exploration Tokens during the Quest phase as well. So if a hero moves into an area with a face-down Exploration Token during a Strategize or Mobilize, for example, it does not flip over.