Check the space to the left near the exit to find a hidden Earth Drum. There’s an adventurer and a shop to the eastern side of Starkfort’s entrance. Upgrade your gear if you need to then find the hidden Stardust near the ram.
1F
The chest to the left of the entrance has 500pg while the other one in the middle-right has a Hi-Potion. After the scene, you’ll get a new party chat. (Faltering Foreknowledge) The middle gate is locked so you can either take the northwest or northeast stairs.
The northwest stairs lead to a sub-scenario where you have to defeat the Salve-maker Qada while the northeast stairs will lead you to Egil. If you want to rescue Egil first, then you can take the northwest stairs, grab the 1000pg from the chest and save your game. For details and tips for defeating Qada, follow this link.
2F
After taking the northeast stairs, grab the Ice Brand from the chest along the way and head to the left to find Egil. After meeting him, a new party chat will be available. (Rescuing Egil) Ignore the other chests in the 2nd floor since you don’t have any ways of accessing them right now. Head back to Hartschild.