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I just went and watched the lesson and yes he is hitting 2 strings for each strum. It’s not obvious from watching but I can tell by listening to it and the fact that there would not be any change in the pitch if he was only hitting the open string.
As for your fingers, it’s not a hand size issue, it just that you are just starting and your fingers haven’t stretched and loosened up. This will happen, but it will take a while, so don’t worry too much about it at this point. It’s ok to either slide you fingers up, or use your pinky. Most people have problems using the pinky but it’s not strong enough in the beginning, but that works for you then great, you building it up even more.
The goal is here is to give it a good try, but don’t strive for perfection, when you have give it a try, move on to the next lesson. It’s progress over perfection.