It's not that you're making tons of grave errors. (Attacking a bit too early every now and then isn't really big.) It's just that Ganon does a lot better against Zelda than he does Sheik. When you play the very common Sheik/Zelda combination, that is, using Sheik to damage and Zelda to kill, you end up with a sound strategy. This should, as you believe, translate into a very nice fight for you against Ganondorf.
I'm going off the assumption that Sheik was the first one for you to learn. First off, when you're going for the kill with Zelda, try to limit your use of fair/bair. Lightning kicks for that style of Sheik/Zelda are not the best thing to go with unless you're using those kicks when someone hits your shield or if you know they'll land. You approached with them, and they're horrible aerials to approach with.
When Zelda gets knocked in the air against... well, most of the cast, unless you really know what you're doing, do not attempt to fight back. Dodge and move AWAY from them. Zelda's floatiness doesn't allow her to airdodge past someone like Ganon, as we saw in your second video. If you must try to pass them, use Nayru's once in order to slow yourself so whoever is trying to hit you from below will be falling back down before you reach them. This will help you get to the ground safely. Make sure you can't be reached when you use Nayru's.
Really, you aren't doing too bad. Zelda is just so freakishly light and so easy to manipulate in the air. Ganon hits very hard, too. Stick with Fsmash and ftilt to keep Ganon away from you. Usmash works whenever he's above you of course. Dsmash and dtilt are also good. The idea is to not jump. You can use Din's from a distance to try and get him to move towards you, but if he does not move, close the distance but don't get in striking range. I like to take steps back and forward and spam Fsmash because it's a pretty safe move in general. If you must approach in the air, use nair. Don't use fair/bair.