The first question doesn't have a short answer, and it's really freaking hard to explain. Especially since I have no idea how many of these thing you may or may not have done already. A walkthrough is what you want. There are multiple subquests which need to be completed for some parts.
To enter the Hall of Echoes, you need four things.
1) A spell, which is found in the Battle Tower in Maxos' bedchamber. It's a piece of paper which glows.
2) A shield, which is given to you by Zandalor in Aleroth, after you defend him while he is closing rifts. To get to Aleroth, you need to take the Zeppelin in Champion Harbour.
2a) The Zeppelin fleet is out of order, you need to find 3 Zeppelin parts - a Compass, a Hover Crystal, and a Rudder. They can be found in some Wyvern nests in Orobas Fjords.
3) A sigil, which is held by the Demon Baal. Fly to Broken Valley and look at the fortresses near the old mining guild. One should have a hatch going underground. That's the old mine. Explore it and defeat Baal for the sigil.
4) An entrance. Under the waterfall by the statue in Orobas Fjords is a cave. Explore it and you'll come to statues. They'll tell you they want seeds. Go see the respective trees and complete the tree quests, once you have all three seeds, go back and give them to the statues, then go through the door until you find someone who can open the entrance.
As to the second question, I don't have any idea what the Champion Harbour fight room is.
