Here's my opinion on all the cards.
Elven Scout - The way I understand it is if she's enraged all your cards count as if you've comboed them. What happens if she takes damage and dies? Do you still have combo for that turn? This is overall a really good card.
Undercity Messenger - I love it. The amount of synergy it has with the Rogue class is amazing and it even looks to be perfectly balanced.
Fungal Companion - This one might be a little too strong. You're essentially drawing a really good card upon its death without milling your deck. I'd consider making it a 3/2.
Crazed Cultist - This one feels like it'd fit more in the mage class what with their mastery of spells. Either way, her stats are too good for her effect. Bumping her up to 5 mana feels appropriate. If you compare her to Azure Drake, you don't get the spell damage but you can combo her for the reduced mana cost. A random card is still drawing you a card.
Nerub'ar Weblord - We already have a minion with this name but other than that a solid card.
Arcane Zapper - It looks good.
Dual Talent spec. - You should consider giving the second use of this card something to do like Shadowform. I really like this idea.
Finishing Touch - Honestly, this could be +4 attack since you are also losing one durability.
Rethiel the Greenwarden - Restoring health feels a little odd for the Rogue class but other than that it's a nice card.
Icecrown Healer - I like the concept. It's a little similar to Armorsmith in stats and ability and it works well with the Priest's other cards.
Dunehill Gravedigger - His deathrattle either restores all minions to full health or deals 1 damage to them? The randomness seems a little odd but it still looks balanced.
Razor Hill Priest - Windfury is kind of the Shaman's thing but the stats are balanced, especially considering the Shenanigans Priest can pull of with this.
Psychic Scream - The flavor and balanced are both good but I wouldn't personally give Priest a card like this. They already have some of the best removal in game and adding Sap to their repertoire is kind of broken.
Trolling "Medic" - I absolutely love it. The quotation marks, the flavor, the way you could potentially heal him back up and proc the enrage again. it all fits Priest quite nicely.
Mind Sear - Will the target take damage if you have Spell Damage? Remember that even 0 increases with it. For example, using Shield Slam with an Azure Drake out and no armor still deals 1 damage. If you want it to deal no damage to the target whatsoever it should be worded as "Deal no damage to an enemy minion and 2 damage to all other ones." Other than the ambiguous wording this card is very good.
Witch Doctor - This is actually extremely weak. Playing it on turn 3 would almost guarantee instant removal so you'd need to combo it with something. However, heal effects only take place if you heal something that's already damage. You'd need to either reduce the cost (even 1 mana could be appropriate) or bump up the stats to, say, 1/4.
Maghdatar Runist - His effect could be worded as Enrage since that's effectively what it is. Pretty solid card otherwise.
Highpriest Zondar - This guy is a little off. Why would you want to restore health to enemy minions? If you say he combos with Auchenai Soulpriest he will also damage your side with his effect. His stats are also pretty weak for his cost. I'd consider swapping them and making him 4 mana. That way he's a little stronger than a Yeti but it's justified since he helps your opponent more than you when he comes in.
Air Elemental - Being random means it could also target itself and then instantly get removed. With the power Windfury has I think he's at exactly the right place.
Soulreaper - Turning Overload into an advantage, not bad.
Highland Elemental - It could have some kind of effect like Water Elemental does. After all, they are the same cost and similar stats.
Enchanted Acolyte - His stats might be 1 point too high but I think he's good. There are still ways for him to be removed for the same mana or less (Fireball, Shadow Word: Death) leaving you behind so it's justified.
Tremor Totem - I would consider dropping its health to 3. Soaking up removal is good enough but it shouldn't be able to take 2 spells easily. Shamans also have lots of Taunts to protect it so dying to minions is a bit hard.
Vengeful Spirit - This one is way too strong. 4/3 for 3 mana is already good on its own but it also gets you a discounted card upon death? An overload of 1 is not enough to justify this power. I'd make the mana cost 4 but keep the card the way it is. Compare it to Gnomish Inventor: 4 mana 2/4 draw a card. You'd have: 4 mana 4/3 Overload 1, draw a card on death and it costs 2 less. I think it's pretty balanced.
Molten Protector - This is also too strong. An overload of 2 usually means decreasing a card's cost by 1 so you already have a 5 mana 5/6 with Taunt which is incredibly good. Drawing a card on top of that makes it too valuable. Its mana cost would need to be at least 6 to justify its effect with these stats.
Chain Heal - If it can target the same character multiple times, i.e. your hero, it's good. Otherwise, it's too weak and should cost 1 less.
Overload 3k - This is actually too weak. You'd need to have at least 3 overload crystals for it to be worth it and that means you're already on turn 7 when a 6/6 is less than threatening. I'd make the effect +3/+3 for it to have some impact as a legendary and also make it so the stats can't be silenced off. Since you gave it X/X stats it could transform into its proper ones like Druid of the Claw does.
Icecrown Defender - Overall balanced.
Flameforge Defender - I think he could have Taunt without it being an Enrage. How about "Enrage: +1 Attack and Taunt" instead?
Worgen Vanguard - It's probably good.
Flameforge Squire - I like the idea.
Silver Hand Arcanist - Spell Damage is not really the Paladin's thing but it's good for a class card.
Sanctuary Guardian - Restoring 5 health to your hero costs roughly 2 mana as seen on Guardian of Kings. Adding Divine Shield to that makes this card just a bit too strong. I'd consider making this a 4/4.
Highland Safekeeper - He looks good though since Enrage is a persistent effect you should word it like Dire Wolf Alpha "Adjacent minions have +1 Attack".
Divine Blessing - I like it. Good for trading though it requires some board presence first.
Muradin Bronzebeard - A really good legendary card. I could even contest Dr. Boom for the 7 mana slot. Summoning extra Recruits could easily get out of hand with all the combos Paladin now has for them making him a high priority target. What's more, they are summoned at the end of the turn meaning you have 2 of them ready to attack with him immediately. His stats and Divine Shield are also at exactly the right place for him. The only thing bugging me is Muradin is not actually a Paladin but a Warrior :P .
Chained Nazvor - Balanced. Nothing more to say here, really.
Amani War Tiger - Really good against aggro decks, not so much against control. Houndmaster him and watch zoo and mech mage concede. I like it.
Volley - A mini Consecration. It feels right where it currently is.
Longshot - Savagery for Hunters only it doesn't suck since they actually have weapons. I like the idea and the balance is right.
Cenarion Gryphon - I love the idea, it's balanced, it synergizes well with many of the Hunter's cards, it's really well-thought.
Cursed Toad - If by Corrupt you are referring to the Warlock's Corruption then this is really good. I'm not too sure about giving Hunters overload though.
Little Game Hunter - This one is too strong. There is a huge number of 2 mana minions with 2 attack. Dropping him down right after your opponent's Mechwarper, Shielded Minibot, Mad Scientist, could really turn a game in your favor. I'd consider making him a 2/2 that only targets minions with 1 or less attack. A little more situational but there are still plenty of targets.
Warsong Cannoneer - By shots you mean the Hunter spells that have Shot in their name like Arcane or Cobra? By reducing their cost you instantly get 4 mana back and 2 pretty powerful cards. I'd consider making it just one Shot or remove the reduction in cost.
Al'ar - It doesn't really feel like a legendary. Copying Malorne's effect on it doesn't really give it much.
Arcane Scholar - The mage's hero power is a really powerful too. Disabling it as a cost for tempo gain feels appropriate.
Arcane Skullmage - Mages already have Soot Spewer for a 3 mana cost minion with Spell damage. This is just a better version of that without being a mech. I don't think they need more of the same thing.
Spawn of Ragnaros - Nice idea. You can time him right when you are planning a turn with 3 leftover mana to maximize your Fireblast's effect and gain a small advantage.
Arcane Apprentice - Once again you underestimate the cost of drawing cards. This is essentially a 4 mana 3/3 that draw you 2 cards without milling your deck. What's more, you know those cards are going to be spells and Mages have ways to benefit from that. She should cost at least 5 mana.
Elite Arcanist - I compared him to Piloted Sky Golem and he feels balanced. He might cost 1 more mana and have worse stats but you know you are getting an incredibly powerful 4-drop instead of a random one and the Spell Damage is nothing to laugh at.
Arcane Blast - Pretty good. We might actually see people using Arcane Missiles more often.
Electric Sentry - I like this one. It essentially has Taunt since your opponent can't ignore something like that. Drop him on an empty board and you might even see him soak up a Fireball.
Lunargift - I think it's good since it requires you to have a minion on the board already.
X-zan the Time-lost - This looks like something you'd see in Freeze mage. Weak to silence but otherwise a really strong board presence.