Investigate the Dungeon Entrance

This one gave me a bit of trouble. Here's how I got mine to complete, and this worked for some other people too.

Get the quest from the fairy outside the castle. Fly into the castle and look for the stairwell behind the throne. Fly down the stairwell (it turns to the right) and look for the entrance at the bottom. Fly your mount into the doorframe and wait 30-60 secs.

Also, they ask you to investigate the throne. The spot you need is right in front of the throne at floor level, not throne level. I believe you can stay in your flying mount for this.

TIP: When it asks you to kill the mobs in the dungeon, fly all the way to the back of the dungeon. Get extra soul force orbs ready. Land, run into the mobs, and hit your sf. Recharge your sf as fast as you can with the orbs, and sf again. This should give you the amount you need. Run to the back wall before they respawn. Get back in your flying mount and fly out.
You can use a double sf attack for the Undead Lieutenant as well.