Right. You want player and character to be in harmony. You can't have the player coming up with stuff that the character wouldn't know, because that's meta-gaming. The character also does know a lot of stuff that the player doesn't know, though, and that shouldn't be discounted.
I agree. The character should know stuff that the player does not know, but at the first hint of an intellectual problem, it shouldn't necessarily be "pick up the dice and roll". The DM should just tell the player some things the character knows and move on. Let the players play the game. The character is irrelevant. It's the players who are in the real world there to play the game and have fun. Let them do so. But, don't hand info out on a platter. Give the players a chance to play, give them some pertinent info, but let the players solve the problems and puzzles. Having the character and the dice do so defeats the purpose of roleplaying the character.
The character is the one who actually exists within the game world. The player has no agency within the game beyond what the character can do.
True, but that's a really long list of possibilities.