For the disappearing platform section, you can use the headbutt midair to pause and give you time. Find the platform you want to jump on as it disappears, double jump to it, headbutt, and by the time you drop from the headbutt animation the platform will have reappeared.
You can also use this to hover above a single platform if you need to plan some things out. Just double jump straight up and headbutt and you'll land back on the same platform as it reappears.
I don't know if that's how they meant for you to do it, but that's how I did it.