Can cards like behind strong walls and the leadership readying a single ally card target other players allies? Or do they have to say the word "any" like the card that moves resources from your hero to another or exhausts your hero to ready another.

Yeah, it can target characters from any player. It doesn't need the word "any." If it were restricted to your own characters, the card would need to say something like "a character you control."

Unless otherwise specified, the only effects on cards restricted to you as an individual player is a cost. You can't play "We Are Not Idle" and exhaust another player's Dwarves to generate additional resources.