For Barnabus' cave, there are 3 teleporters you need to explore. The top one on a high ledge leads to a cave with 3 sections, the mid level teleporter and ground level one each have a generator that needs to be disabled.

In the dragon cliff castle, you need to talk to Jedediah (the guy at the hatch) and retrieve the items he needs.
The Drudanae can be found in High Hall (read Nicolas' mind...) and the Chalice of the Dragon is in the slayers' camp near the harbour (you can trade Lord Arben's sword for it, fight or mindread).

You can not enter the champions' clubhouse.

Chests that can not be lockpicked require a key or a password. There are a couple chests with no keys (one half buried in Maxos temple's maze, one in Keara's flying fortress...), but you should be able to get most of them.
Treasure Hunter Chronicles: Ultimate locked chests