With the gate skip, when going to the right you want to use the lamp that's just underneath the platform and try to wedge yourself on it. The hitbox for it is kinda weird so you'll probably end up falling down sometimes when it looks like you should land on it.
When doing a double jump attack you can press two character swap buttons (L/R) in quick succession in order to swap out and turn back into your character to cancel the end lag.
Hopefully this helped, if you need more help I'd recommend joining the LEGO Speedrunning Discord, since you will normally get a response pretty quick, and it's easier to explain things than in src forum posts.
To add to what's already been said, basically whenever you want to cancel an animation and character swapping is available, that's what you should do.
We have a discord which you can join, it'll make it a lot easer to learn new things.
