Head voice, high notes, and vocal warm ups

Hey Camille! I have almost been taking these lessons for about 25 days and am seeing some improvement in my voice. I have a few concerns. I notice that during the warmups in the beginner and daily warmups, my voice cracks when I get to the higher parts of my range, or sometimes even when I try to sing a single note, but my voice doesn't really crack when I am singing a song. How can I stop the voice cracks during the warmups? Also, I think I am starting to understand head voice, and have been trying to apply it to my song work for the higher parts. I thought about singing higher notes in head voice, so I tried. Before I thought about singing them in head voice as like getting quieter and doing like a loud whisper while trying to raise my soft pallet and drop my jaw. But then I realized I was more so doing falsetto whenever the sound came out airy. So I am trying to work on focusing the sound as resonating through the mask of my face, getting quieter or trying to keep the same volume, dropping my jaw and trying to raise my pallet. Is that a good way to think about singing in head voice? I also heard people say engage your abs when you sing in head voice, is that true? Lastly, during warmups I notice that, like you said, getting quieter makes it easier to sing the higher notes, but they sound like really airy falsettos or just weak. Is me approaching high notes like this instead of pushing for the notes going to help me extend my range in the long run? Sometimes I feel like if I can't sing a high note in full volume, I'm not really doing it. 

Here's a lesson on cracking for you: https://www.youtube.com/watch?v=32Ik5f7RytA.

It's okay for your head voice to be weak/breathy in the beginning, but you can encourage strongeer cord closure with semi-closed exercises. Here's a lesson on strengthening head voice: https://www.youtube.com/watch?v=lBWSHk06n74.

Hope those help!