TLDR; Your assumptions are correct - you can 'automatically' draw three cards on a successful quest with three Expert Treasure-hunter attached to your heroes and a Gandalf (hero).
To answer your first question, yes. If have Gandalf (Hero) and Expert Treasure-hunter attached to a hero when you quest successfully on Expert Treasure-hunter's triggered ability activation you can name the type of the card on the top of you deck, then discard and draw it.
For the second question I think the key is Gandalf's
Play with the top card of your deck faceup. This means that the top card of your deck (provided your deck has cards in it) is ALWAYS revealed as long as you have Gandalf's ability. Thus during each activation of the three Expert Treasure-hunters the top card of your library will be revealed and you can name its type, then discard and draw it. Id est you can automatically draw three cards on each successful quest with Gandalf and three Expert Treasure-Hunter's attached to your three heroes.
The source for my interpretation is the "The Lord of the Rings: The Card Game Online Rules Reference" found on the Fantasy Flight Games website. In particular the second Golden Rule (page 2):
If the ability text of a card directly contradicts the text of either the Rules Reference Guide or the Learn to Play book, the text of the card takes precedence.
implying that the top card of your deck is ALWAYS revealed if you have the Gandalf hero's ability. And the definitions of Response (page 14):
Response abilities are labeled by the word “Response” followed by ability text. Unlike action abilities, which are resolved during action windows, response abilities may be executed after the specified triggering condition occurs, as described in the response’s ability text.
- It is possible for multiple responses to be executed from the same triggering condition.