I actually was thinking of doing a similar thing for all the classes, so I guess I can leave out Warlock.
A few things I don't agree with:
Searing Pain seems like a straight up nerf for no reason. There's absolutely no scenario in which I'd want to play this over Shadowbolt. having to wait for a turn to remove a minion is just not really something that has ever been played and in comparison to Corruption it just looks terrible.
Searing Pain says at the start of the next turn, not the start of your next turn. So the minion would be dead before it gets a chance to attack again. The only way this is different than just "deal 4 damage" is if you want to clear a taunt or something.
Honestly though I would just leave Shadow Bolt in the basic set, there is nothing wrong with the card. It is a lot fairer and simpler than Searing Pain. I really don't see the need for the change.
10/10 card. 3 life and heal for 3 is worth 2 mana, so playing this for 3 isn't even that bad, especially for a class that wants to heal as much as Demon Hunters do. And if you can get this for 0 mana, it can swing the game in your favor.
The outcast mechanic is actually a lot easier to activate than I once thought. Turns out that playing cards is quite easy for dhunters, and they're not exactly low on draw neither.
I think the Gadgetzan Auctioneer synergy doesnt make much sense since dhunters can already draw pretty fast all on their own. Its like 3 or 4 cycle cards and on top of all that is Skull of Gul'dan, practically a mini, slightly more expensive wondrous wand. Dhunters can probably play Chef Nomi with no support other than their cycle cards, just speculating.
The biggest difference between Blur and Time Out! is that the latter is active during your opponent's turn (when you would normally take the most damage), while Blur only protects you from damage taken on your own turn (normally from attacking things with your hero). In other words Blur is like a heal, but it does not guarantee you will live 'til your next turn.
The difference with freezing ends up practically non-existent, since the minions with freeze effects normally have to deal damage to freeze, so attacking them and taking 0 damage prevents that problem (I assume).
Neoguli's Custom Warlock Core Set Changes
Searing Pain says at the start of the next turn, not the start of your next turn. So the minion would be dead before it gets a chance to attack again. The only way this is different than just "deal 4 damage" is if you want to clear a taunt or something.
Honestly though I would just leave Shadow Bolt in the basic set, there is nothing wrong with the card. It is a lot fairer and simpler than Searing Pain. I really don't see the need for the change.
Demon's Bite
I see Illidan Stormrage finally prepared ^^
Demon Claws
Was that why we was warning us to get ready and prepared for?
New Demon Hunter Spell - Eye Beam
10/10 card. 3 life and heal for 3 is worth 2 mana, so playing this for 3 isn't even that bad, especially for a class that wants to heal as much as Demon Hunters do. And if you can get this for 0 mana, it can swing the game in your favor.
Our Thoughts on Hearthstone's Upcoming Demon Hunter Initiate Set (Part 1)
Woopsie! Good catch on that! I think that was one of my last reviews on the day I did it, so the this turn part flew over my head.
Our Thoughts on Hearthstone's Upcoming Demon Hunter Initiate Set (Part 1)
Blizzard should ask you guys to make flavor texts for cards in the next set.
Our Thoughts on Hearthstone's Upcoming Demon Hunter Initiate Set (Part 1)
I much rather play Ur'zul Horror on Turn 1 and hold onto Battlefiend for a midrange combo
New Demon Hunter Spell - Eye Beam
Talking about looks that kill ^^

New Demon Hunter Minion - Illidari Felblade
Rush with Conditional Immunity is a cool design
New Priest Minion - Psychic Conjurer
Reading your opponent's hand in disgust ... a Wisp !?
Our Thoughts on Hearthstone's Upcoming Demon Hunter Initiate Set (Part 1)
The outcast mechanic is actually a lot easier to activate than I once thought. Turns out that playing cards is quite easy for dhunters, and they're not exactly low on draw neither.
I think the Gadgetzan Auctioneer synergy doesnt make much sense since dhunters can already draw pretty fast all on their own. Its like 3 or 4 cycle cards and on top of all that is Skull of Gul'dan, practically a mini, slightly more expensive wondrous wand. Dhunters can probably play Chef Nomi with no support other than their cycle cards, just speculating.
New Priest Spell - Power Infusion
It infuses, it enthuses, it amuses!
New Priest Minion - Natalie Seline
Cool effect - no Prophet Velen level of greatness - but a cool replacement nonetheless
New Priest Minion - Kul Tiran Chaplain
Well, I have some time on my hands ... ^^
New Priest Spell - Shadow Word: Ruin
This ... is ... AMAZING

New Priest Minion - Scarlet Subjugator
That's a cool 1-drop, but won't ever replace Northshire Cleric
New Demon Hunter Spell - Soul Split
'' Spoiler: they're both the evil twin. '' ^^
New Demon Hunter Spell - Feast of Souls
'' Nothing fills you up like soul food! ''
New Demon Hunter Minion - Wrathscale Naga
Of course, some Nagas will perish ...

New Demon Hunter Spell - Command the Illidari
6 [Hearthstone Card (Illidari Initiate) Not Found] for (5) mana is a great deal
New Demon Hunter Weapon - Umberwing
Bats may not be at their all time favorable moments, but the Felwings are pretty cute tokens
Our Thoughts on Hearthstone's Upcoming Demon Hunter Initiate Set (Part 1)
The biggest difference between Blur and Time Out! is that the latter is active during your opponent's turn (when you would normally take the most damage), while Blur only protects you from damage taken on your own turn (normally from attacking things with your hero). In other words Blur is like a heal, but it does not guarantee you will live 'til your next turn.
The difference with freezing ends up practically non-existent, since the minions with freeze effects normally have to deal damage to freeze, so attacking them and taking 0 damage prevents that problem (I assume).
New Demon Hunter Minion - Battlefiend
Thankfully, they are not mutually exclusive, and you'll need a handful of 1-drops to make your aggro list work ^^
New Demon Hunter Spell - Mana Burn
One way to ensure that your opponents are not prepared.
New Demon Hunter Spell - Blur
The heavy DH's weaponry makes a tad more sense given this card