Thought Magic
I'm making a proper pass through the core mechanics now (as opposed to the quick skim from before).
Ideas as Cards
Nothing much to say here. I don't expect all that much more will change here (aside from clarifications) unless the core mechanics need another overhaul.
Expressing Ideas
There's a timing mismatch for IP here. You get a new hand of cards at the end of your turn (which matches the timing of when immediate actions start applying to the following turn's action economy), but you get your 1 IP at the beginning of your turn. Does that mean that if you want to express any immediate action ideas, you need to generate IP for them in your previous turn and carry it over, despite the fact that you don't know what ideas you'll have, if any?
You may wish to clarify that IP from previous turns doesn't carry over into following turns. It sounds like that's the intent by "starts each turn with 1 IP", but it would be nice to have it explicitly stated so you don't have to parse the implications of that sentence to find out.
Can thinking classes be progressed by arcane- and divine-spellcasting advancing PrCs, or just the ones that allow for any spellcasting class to be advanced? You've indicated that though magic meets arcane- and divine-specific prerequisites, despite being neither, but not whether the classes themselves can be advanced as such.
Ideas Outside Combat
I'd remove the part about losing the ability to express ideas without daily rest. Leave the rest requirement in for changing your deck and refreshing daily IP, sure, but it's unnecessarily punishing in some circumstances. Spellcasters don't lose their unused spells if they can't rest, they just don't get to replenish the ones they've used.
Daily IP is weird. You get very little of it, but there's also no need for it, since you still have your base 1 IP per turn outside of combat and by the time you can spend more than 1 IP per idea, you should have at least one idea that generates 2+ IP. I get the impression that this isn't the intent, though, that you aren't supposed to get that 1 IP/round outside of an encounter.
Outside of combat, I wouldn't bar the use of deck- and hand-modifying ideas, just state that those parts have no effects. There are a few ideas with deck- and hand-modifying rider effects.
I don't think you intended to have the free 1 IP/turn apply outside of battle, but if you do keep it or a mechanic like it, make sure it's structured such that players don't feel compelled to constantly refresh their short-duration buffs out of battle, either through a complete lack of free-use buffs that last more than 1 round or through some mechanism that inhibits that play pattern (ex: expressing a combat idea out of combat dismisses all previous combat ideas still ongoing) and/or obviates the need for it (ex: you can maintain 1/2/3 combat ideas out of combat, their durations remaining at maximum as long as their effects/targets remain nearby).
Encounters
I'm not a huge fan of this section. All three things here (locking the deck at the 10 round mark, ending effects 1 minute after combat ends, and penalizing avoiding combat) feel arbitrary. I understand the intent behind them, but they just leave a bad feeling.
If you want to curb the power of a thinned deck in excessively long encounters, perhaps some sort of deck reset mechanism instead, where under some conditions retired ideas as reshuffled into the deck (ex: move it to the discard pile after 1 minute or 5 deck shuffles or something)?
If you want to keep players from picking fights with rats so that they can buff up, don't make long-duration buff effects as ideas. You may wish to separate long-term effects (minutes/level duration and longer) from more immediate in-combat effects. Say, for example, you could have your basic in combat ideas with instantaneous and short durations (I'm inclined towards fixed durations of 1, 2, 3, 5, or 10 rounds rather than 1 round/level, personally), but some of them also have "grand vision" effects that allow them to produce long-term effects when you spend daily IP (rename to "Grand Vision Points" or something), which would also let you cut down on some of the arbitrary distinctions between in-combat and out-of-combat expressing.
I don't see the need to penalize players for taking the time to thin their deck and prebuff if they know an encounter is coming up but haven't actually engaged. That's just the standard benefits of preparation for an immediate upcoming encounter, like spellcasters unloading all their round/level buffs. You also don't want to encourage DMs to penalize players for avoiding combat legitimately, such as during stealth encounters or when attempting to retreat or flee.
Multiclassing
Multiclassing is a major nerf to a character, even without the lost thinker progression. You pad your deck with lots of lower-level ideas just by taking a single level of another thinker class. I'd just have each thinker progression give you a completely separate deck, rather than merging them all together, and have any deck manipulation from an idea associated with a deck only apply to that deck (ex: expressing Being Meta drawn from your Creative deck would only let you search your Creative discard pile). Hand size would either be separate for each class (ex: Creative 9/Strategist 4 draws 5 from Creative and 3 from Strategist decks each turn) or stacks class levels and lets you divide your draws between decks as you see fit (ex: Creative 9/Strategist 4 draws total 6 cards per turn divided as they choose between the two decks).
Changelog
I like change logs.