2. There is no genuine 'puzzle solving' in Ico.
This is how you solve a puzzle in Ico: look for an object that you can do something with: i.e. a block. Then put that block in the nearby floor-button. It helps because there is only one floor button to put it in, so essentially you can't get it wrong. One block, one floor button. It's about as linear as puzzle solving gets, and so much of the game is like this.
If you see a rope, you climb up it, which takes you to a platform. At this point, there's no lateral thinking involved to get to the next platform, it's simply a case of pulling a lever/climbing a foothold. There's never a choice between a lever and a foothold, as the game is so simplistic and linear that it's practically on rails, and it pretty much directs you where to go itself.
In comparison, with Portal 2 you have to use your HEAD to think about how to solve the puzzle. It's not a case of 'I need to push this floor-button, oh obviously I do it with the block that is sitting 2 feet away', it's a case of 'HOW do I keep these two buttons pushed down when there is only one block, and even that block disintegrates every time I try to bring it across the barrier, and to make it worse I have to do it whilst avoiding the gun turrets. But I have at my disposal a portal gun and some paint which allows me to turn regular walls into portal-walls'. Essentially, you can't just sleepwalk through Portal 2. You have to solve the puzzle. Not sleepwalk through the puzzle.