Wojtek addressed most of your questions, but I'm just going to add details to this one question.
**Are there certain cards that are more cost effective to DE? **
There are two things that affect how much dust you get when you disenchant a card.
- Card rarity
- Foil/non-foil
Card rarity can be found by looking at the gem in the center of the card. Common cards have a white gem and give 5 dust when you disenchant them. The colors match the colors in World of Warcraft, with the highest being orange (legendary). Cards that are more rare will disenchant into more dust (you can see how much as Wojtek explained). Also, the cards you get as you level your hero to 10 are considered "basic" cards and don't have a rarity gem. They can't be disenchanted.
- Normal Gold
- Craft DE Craft DE
Common 40 5 400 50
Rare 100 20 800 100
Epic 400 100 1600 400
Legendary 1600 400 3200 1600
If you go through the math to complete a complete set of 2 copies of every card (leaving all of the disenchanting and crafting until last), you're much more likely to need to disenchant commons and craft legendaries. source
Sometimes you can find gold (foil) versions of cards when you open packs. These cards functionally play exactly the same, but if you disenchant them (and keep the non-gold versions of the card) then you'll get more dust. On the other hand, gold versions are animated (some are QUITE nice) and a nice thing to show off.
So, to answer your question, it is generally more cost effective to disenchant the gold cards, if you don't care about the aesthetics and status of using the gold cards.
Another fact to note, if you use the "disenchant extra cards" button, it will automatically keep 2 regular and 2 gold copies of each card (for a total of 4 copies of the card). You have to manually decide which cards you want to keep and disenchant the others.
There are a few that comes to mind.
Board clears/AOE: obviously when you have a lot of low mana weenie creatures, they are highly susecptible to board clears. I've started to bring 2 Wild Pyromancers into every deck just for those situations. Each class have their own way of doing board clears but they are all quite effective at killing the minions. Zoolocks typically counter this by packing lots of divine shielded minions, so I also started packing a blood knight into my decks for this purpose.
High Health Taunters: With only limited hard removals, if you put out enough taunts then he will lose a lot of minions in trying to remove your taunter. 5+ hp taunters is best since it can survive a soulfire.
Weapons: You can limit his board control by clearing out his weenie creatures via attacks. This isn't for all classes but rogues and warriors excel in this regard.
As an aside, abdomination does both #1 and #2 so it is especially good against zoolock.
Best Answer
No. Your card collection has absolutely no correlation to the cards you can pick in the Arena. In fact, you can end up with Arena decks that are illegal (for example, because they contain more than two copies of the same card), depending upon what random cards are presented to you and the cards you choose.
The random cards presented to you will be from all the non-promotional cards available in the game, regardless of whether you currently have a copy of that card or not. This means that you can expect your opponents to have any possible card in the game as well, which makes for a bit of a different strategy / play style than regular match play.