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.
Best Answer
From the Hearthstone wiki (emphasis added):
It was introduced in the December 4, 2018 expansion.
As for strategies, I believe that that is a very broad question, but a player could use it to gain tempo by slightly Overkilling a minion to summon another, such as using the 5 mana Baited Arrow to kill another minion with 2 or less health remaining, to summon a 5/5 Devilsaur at the same time.
Ironhide Direhorn looks like another good card if it could survive a turn/attack immediately, perhaps when combo'd with Rush to let it Overkill a minion and summon a 5/5 Ironhide Runt.
Personally, I think Totemic Smash looks like it will give the best value for a Turn 1 play if the opponent plays a card with 1 HP; or it could also be used to remove another minion if you lack 1 HP to kill it with your other minions on board, in order to Overkill by 1 HP.