Irix the Wanderer - His plus ability should be the "regrow a spell" ability. You could add "at random" to it if you wanted to power it down a little. I think I'd then try Fork (Reverberate) as his minus ability. The ultimate could remain the same and overall you'd have a much more synergistic planeswalker. Like this:
3UR / 4 loyalty
+2: Return an instant or sorcery card at random from your graveyard to your hand.
-2: Copy the next spell you cast this turn. You may choose new targets for the copy.
-9: Until end of turn, you may cast spells in your hand without paying their mana costs.
Primal - What if you got the bonus if you cast the card using only one color of mana? Like the opposite of Sunburst. "If you spent only white mana to cast CARDNAME..." This solves the non-basic land problem nicely, because lots of nonbasic lands make colored mana (obvious, I know). A few constructed-quality primal cards could also be interesting stressors on deck building. You can play two colors, but you'll want to be sure all your lands can produce the primal color you're looking for (again, upside for non-basics instead of downside). Neat how one simple change can keep the essence of this mechanic and sweep away the flaws.
Liliana of Shadow - how's this:
3BB / 4 loyalty
+1: Each opponent loses 2 life, you gain life equal to the amount lost this way.
-2: Destroy target creature, you gain life equal to its toughness.
-5: You gain an emblem with "pay 1 life: draw a card."
The first ability is a little bit like Sorin, but it's a lot like Syphon Soul, which predates Sorin. Also, always push your planeswalkers on first design. You want people (in FFL) to play them a lot and you want them to be as powerful as they reasonably can be.
Obscure in Shadow - I don't know why they didn't say it, but you could take the top card of the deck and put it face down instead of the countered spell. That would create cool morph mystery. On second thought, I know why they didn't say it. They don't want to be redesigning your cards, they want you to figure out how to redesign them yourself. In fact, you need to prove that you can do it almost as much as you need to prove you can design cards in the first place. That, or this suggestion still fails the "spells can't be morphs" rule - but you're clearly counting on persuading the rules manager on that front anyway.
Twilight Zone - don't be so fancy and fiddly. Deathbringer Liege did everything you want to do here, just do a variant of that card. Don't be ashamed to re-purpose an old design when it fits your current plan. +2/+2 for a white spell and -2/-2 for a black spell would be pretty saucy. If you want something more elaborate that's fine, but the fastest way to junk up Magic is by throwing around unnecessary counters.
Library Raid - I would do this:
Draw X cards, then discard 3 cards, where X is the number of attacking creatures you control.
Accomplishes your goals, and Alexis would play it in a deck. If you mean "attacking creatures" then say it; don't say "tapped" and make people figure it out.
Bladetooth Totem (fixed)
Tribal Artifact - Beast
G,T: Target Beast creature gets +3/+3 until end of turn.
You should do the most basic thing when it serves your purpose. +3/+3 might feel boring to you, but every set needs "boring" cards. Being too fancy is the mistake the GDS2 contestants will make the most often. My rewrite of this card is simple, obvious, and also a perfectly printable uncommon magic card (in a tribally themed block).
The Venser, Planar Guide design made me think of this card. It's tangentially related:
1, T, sacrifice a permanent: Search your library for a permanent with converted mana cost one more than the converted mana cost of the sacrificed card, and put it onto the battlefield.
Yes, the name is a reference to Dominion.
Drothar Deftblade deserves mention as one of the few truly cool ideas in all of GDS2 so far. Now since we're here...
Creature - Human Assassin
T: Destroy target creature, if you do, put a loyalty counter on CARDNAME.
When CARDNAME has 2 loyalty counters, flip it.
Creature - Human Rogue
When CARDNAME deals combat damage to a player put a loyalty counter on it. Etc.
The flipped half is fine. Don't let them bully you too much about what can't be done for technical reasons. All Mark does is assault the rules manager with things that can't be done, he's not one to talk. As for it all fitting, we got levelers to work out. It took a ton of work, so you can only afford to do it when it's really awesome and worth it, and only on one mechanic per set. If you keep going with this be sure to balance it with extra simplicity elsewhere.
Thought Watcher - an easy one to fix:
Creature - Merfolk Spy
When CARDNAME enters the battlefield look at the top 6 cards of target opponent's library and exile one of them face down. Put the rest on the bottom of their library in random order. Whenever an opponent casts a spell you may reveal the exiled card. If it shares a name with that spell, draw 3 cards.
It's a little long, but retains all the mystery. Note that I specifically avoided searching the opponent's library. Doing that would take a lot of time. Worse, it would give you too much information about their deck and possibly their hand. It's more interesting if you only get a limited selection of their deck to work with. Both you and your opponent gain a lot of mystery and excitement this way. There's an initial hit or miss moment for you, and then they don't know if their best card was in the six you saw.
Ace of Ants - another easy fix:
Creature - Insect
Revelation - whenever CARDNAME is revealed from your hand you may pay 1G, if you do, put two 1/1 green insect token creatures onto the battlefield.
I'm sure Daniel had a good reason for Revelation to only work when things you control reveal cards in your hand. I'm also confident that he's wrong. Why not also trigger when your opponent's make you reveal it? It's a hilarious little trap against cards like Blackmail. Naturally, I also took the advice of the WotC crew and made the result simple: always two dudes. You could make it 3 or cost just G, whatever. If you're desperate for the "big X upside" (which is a fine thing to want) you could have it related to the CMC of the card (not "spell") that caused the reveal; "where X is equal to the converted mana cost of the card that caused you to reveal CARDNAME from your hand," but I'm not entirely sure the rules manager will be okay with it. Well, put it in the file and hide when he reads it.
It might also be interesting to have a few colorless-only Revelation costs - those cards could be used the way colorless cycling cards are used in any deck, even when you can't cast them.
Showdown as a mechanic needs work. It's a cool concept that's awful as written. Here's a possible fix: "Each player in the showdown reveals a card in their hand, simultaneously. The player whose card had the highest converted mana cost scores a point. Repeat this process two more times. The player with the most points wins the showdown."
This may have flaws, but it does also have strategy, and might be super fun. Try it.
Arathori, The Spellspinner
Creature - Spider Wizard
When CARDNAME enters the battlefield, for each creature you control, reveal 3 cards from the top of your library and put an enchantment card revealed this way onto that creature. Put the rest of the cards on the bottom of your library in random order.
I'm not totally sure I got the wording right, but again, a rules manager or the templating team can help you. As Alexis said, development can find the right number of cards to reveal, so I just stuck with 3 for now.
I was trying to fix Jonathan's Swarm mechanic when I came up with this:
Shadow Clone - when CARDNAME attacks, put a 1/1 color name token creature with "this creature must be blocked" onto the battle field tapped and attacking.
Naruto fans rejoice! Which also reminds me, one of you should bring back ninjitsu, that mechanic is cool and needs to be rescued from the other memories of Kamigawa.
Well that's it for me for today. GDS is always fun to follow along with!