1. Quests currently cannot be removed. There are no cards to remove them. Supports are removed when destroyed. Examples of cards from the Core Set that can destroy a Support are Demolition (Dwarf), Pillage (Orc) and Burn it Down (Neutral) to name a few.
2. Nothing happens to the units, supports, quests or developments in a Burning zone. That zone still functions and provides power as before. Burning is simply a means of determining victory.
3. Yes you can play both in the same zone. There is a little symbol next to the name of the card that indicates its unique. Look at Grimgor Ironhide (Orc) from the Core Set as an example of this symbol or the Dwarven King (name escapes me.) Only one of a Unique card can be in play at a time.
4. When you see Quest in italics there it means the Forced effect can only be used when in the Quest Zone. The Dwarf Ranger can be played in any zone. Units will say "quest zone only" in their text if they can only be playing in a specific zone. Huntmen (Empire) are an example.