Here’s what we know so far, feel free to jump into the comments to add anything!
 30 cards
 18 specials and 12 basic. Sinbad is an exception at 17 and 13.
Special cards for Heroes and sidekicks:

 Specials are split between the Hero and the sidekicks, except in Bruce Lee’s case.
 In terms of card counts for sidekicks, it makes no difference if the sidekick is a single personality, like Merlin or Porter, or a set of sidekicks, like Medusa’s Harpies or Robin Hood’s Outlaws.
 So far, Merlin has the most cards among sidekicks, at 7 cards.
 Porter has the fewest cards among sidekicks, at 3 cards.
Special card mix:

 Every Hero has a “bread and butter,” which is at least 3 copies of one card. This is typically an attack, but not always.
 Every sidekick set has a bread and butter with 2 copies of at least one card.
 Arthur/Merlin has 11 different special cards, which appears to be the most. Bruce Lee has 13, though if you consider his 6 JEET KUNE DO cards to be variations of the same card, then he has only 8.
 Every deck has attack cards and A/D cards.
 Not every deck has power defense. Sinbad doesn’t.
 Attack values: So far, A6 is the highest unmodified attack value, which appears in several decks.
 This caught me by surprise, but D4 is the highest defense value I’ve found so far. That means that A6 is going to do damage every time. There are none of the D12s and D15s that we saw in Epic Duels. Merlin does have 2x DAll but so far, none of the Heroes have anything like that.
 Less direct damage in this game than Epic Duels. So far, I’m not seeing any card do more than 2 direct damage, though I don’t think 3 direct damage would be overpowered. However, I don’t see 4direct damage cards like THROW DEBRIS, THERMAL DETONATOR or WHIRLWIND ATTACK as part of Unmatched. They aren’t so far, anyways, and I think 4 damage (at least without conditions) would be overpowered.
 Alice’s LOOKING GLASS card establishes that you can have quite a few effects in a single card — 3 in the case of that card, from a set of 4 possibilities. This goes beyond Epic Duels, which typically only had 2 effects in a single card, though fans often expanded it to 3 effects.
Special card counts:
Alice (8 cards, 14 total): 3, 2, 2, 2, 2, 1, 1, 1
Jabberwock (2 cards, 4 total): 2, 2
Total: 10/18
King Arthur (6 cards, 9 total): 3, 2, 1, 1, 1, 1
Merlin (5 cards, 7 total): 2, 2, 1, 1, 1
Any (1 card, 2 total): 2
Total: 12/18
Medusa (4 cards, 11 total): 3, 3, 3, 2
Harpies (2 cards, 5 total): 3, 2
Any (1 card, 2 total): 2
Total: 7/18
Sinbad (3 cards including one with 7 variations, 13 total): 4, 2, 7
Porter (1 card, 3 total): 3
Any (1 card, 1 total): 1
Total: 5(9)/18
Big Foot (3 cards, 8 total): 3, 3, 2
Jackalope (1 card, 3 total): 3
Any (3 cards, 7 total): 3, 2, 2
Total: 7/18
Robin Hood (4 cards, 10 total): 3, 3, 2, 2
Outlaws (1 card, 4 total): 4
Any (2 cards, 4 total): 2, 2
Total: 7/18
Bruce Lee (8 cards including one with 6 variations, 18 total): 4, 2, 2, 1, 1, 1, 1, 6
Total: 8(13)/18
Basic cards:

 Basics are 12 card sets, except for Sinbad, who has a 13 card set.
 All are ANY/ANY (A/A) cards that can be used for any character in the set, and for either attack or defense.
 A/A values range from 14.
 Unlike Epic Duels, there’s never more than 1 value per card, never different attack and defense values like an A4D1 or A1D2, at least not so far. Every card is A/A 1 (i.e. A1D1) or A/A 4 (A4D4) etc.
 Typically 4 sets of 3 cards each, but Alice has a 33222 structure, and Sinbad has 33322 to fill out his 13 card set.
 FEINT and REGROUP appear 3 times in every deck so far.
 Here is a complete list of basic cards to date:
FEINT
A/A 2. IMMEDIATELY: Cancel all effects on your opponent’s card.
BOOST: 2
Appears 3x in every deck so far: Arthur, Alice, Medusa, Sinbad, Big Foot, Robin Hood, Bruce Lee
REGROUP
A/A 1. AFTER COMBAT: Draw 1 card. If you won the combat, draw 2 cards instead.
BOOST: 2
Appears 3x in every deck so far: Arthur, Alice, Medusa, Sinbad, Big Foot, Robin Hood, Bruce Lee
MOMENTOUS SHIFT
A/A 3. DURING COMBAT: If your fighter started this turn in a different space, this card’s value is 5 instead.
BOOST: 1
Appears 3x in: Arthur, Sinbad, Big Foot, Bruce Lee and 2x in Alice
SKIRMISH
A/A 4. AFTER COMBAT: If you won the combat, choose one of the fighters in the combat and move them up to 2 spaces.
BOOST: 1
Appears 3x in: Arthur, Big Foot, Bruce Lee and 2x in Alice
EXPLOIT
A/A 4. AFTER COMBAT: Draw 1 card.
BOOST: 1
Appears 2x in: Sinbad
MAXNOME FOE
A/A 3. DURING COMBAT: Discard the top card of your deck. Add its BOOST value to this card’s value.
BOOST: 2
Appears 2x in: Alice
LEAP AWAY
A/A 4. AFTER COMBAT: If you won the combat, choose on of the fighters in the combat and move them up to 4 spaces.
BOOST: 1
Appears 2x in: Sinbad, appears to replace SKIRMISH
DASH
A/A 3. AFTER COMBAT: Move your fighter up to 3 spaces.
BOOST: 1
Appears 3x in: Medusa
SNIPE
A/A 3. AFTER COMBAT: Draw 1 card.
BOOST: 1
Appears 3x in: Medusa
WILY FIGHTING
A/A 3. AFTER COMBAT: Deal 1 damage to each opposing fighter adjacent to your fighter.
BOOST: 1
Appears 3x in: Robin Hood
SNARK
A/A 3. AFTER COMBAT: If your fighter is adjacent to the opposing fighter, draw 1 card
BOOST: 1
Appears 3x in: Robin Hood
Arthur, Big Foot and Bruce Lee all have the exact same basic deck with 3 each of FEINT, REGROUP, MOMENTOUS SHIFT and SKIRMISH.
Alice has a similar deck, but has a 33222 structure, giving up 1 each of MOMENTOUS SHIFT and SKIRMISH to include 2 MAXNOME FOE. So far Alice’s is the only deck to include MAXNOME FOE and it’s possible that it is her card only, but I don’t see why you couldn’t use it, 2 or even 3 copies, in any other basic deck. It is a pretty good card IMO.
Sinbad has a similar deck as well, despite the unique structure of having 13 basic cards instead of 12. He has 3 copies of FEINT, REGROUP and MOMENTOUS SHIFT just like the Arthur/Big Foot/Bruce Lee deck. Then, instead of 3 copies of SKIRMISH, he has 2 copies of LEAP AWAY, which is essentially a slightly stronger version of the same card, and 2 copies of EXPLOIT. Like Alice’s deck with MAXNOME FOE, so far Sinbad’s is the only deck to include EXPLOIT and it’s possible that it is his card only, but I don’t see why you couldn’t use it, 2 or even 3 copies, in any other basic deck. It is a pretty weak card IMO. He’s also the only one with LEAP AWAY but I already have plans to give it to others.
Medusa and Robin Hood both have unique decks, which I find interesting. As they are the only 2 ranged Heroes, it makes sense to me that they wouldn’t have the same basic cards as the other decks — MOMENTOUS SHIFT especially makes less sense in a ranged deck. However, I would think they’d have the exact same basic deck as one another, the default “ranged” deck. I mean, of 5 melee characters, 3 have the exact same deck, and the other 2 have slight variations of that deck. Medusa and Robin Hood, meanwhile, both share the 3 copies of FEINT and REGROUP like every basic deck does, but then they have 3 copies of 2 cards that are so far unique to them. I don’t see why SNIPE couldn’t be shared in both decks, but it isn’t.
In creating a deck with a melee Hero, I would default to the Arthur/Big Foot/Bruce Lee deck unless you had some specific reasons to include another card the way Alice or Sinbad do. I’m considering replacing SKIRMISH with LEAP AWAY for the General Kenobi and Darth Vader decks I’m formulating. I could see myself using EXPLOIT in a deck instead of either MOMENTOUS SHIFT or SKIRMISH, or mixing it in with those 2 in a 33222 basic deck. I wouldn’t mess with a 13card basic deck, personally.
In creating a ranged deck, I would consider either the Medusa deck or the Robin Hood deck, as is, to start. It might be possible to mix and match between DASH, SNIPE, WILY FIGHTING and SNARK, or use a 33222 structure to include more different types of cards.
The effect of Manxome Foe may be reused by other cards, but the card itself is definitely Alice specific as the name of it comes from “Jabberwocky.”
Thanks for the clarification Josh!