I'm confused at how "no encuentro" translates to "I can't find". In my mind, when you are talking about being able to do something, poder needs to be used and it is completely missing from this sentence. I put "Ah, I don't find the car key!" and was marked incorrect. Even though it doesn't sound right in English, that is the literal translation. Can anyone shed some light on when you do and don't need to use poder?
It's not saying that you aren't 'capable' of finding the key. It's saying that you are searching for the key and have not yet found it. Duo doesn't always want direct translations because a lot of direct translations wouldn't make any sense. That's how they would say it in Spanish but for the exact same situation, "Ah, I can't find the car key!" is what we would say in English. Using 'poder' would still make sense but it's not how native Spanish speakers would commonly say it.
Yes, I think that is very common. And I think it started because long ago when one got "the keys to the car" one always got (at least) two keys...one for the trunk and one for the door/ignition. Same for the keys to the house. One for front/side door, one for garage. Or maybe three at times. Point is, it is only young kids who might ask for "the car key", and then will expect that they don't even have to plug it in, they can just push a button in the car and it will go. "I have to insert the key? How quaint".