I would start learning the hollow rock from a tucked position so you learn how to curl under that lower back. Extend from there.
Basically you can do what the 3 year olds learn as a rock and roll. Get into a tuck, hold your knees and rock back and forth. I heard it's something they do in pilates too, hahah. From there open up the tuck angle until you are in that hollow. I would start with the hands on knees, hips, then chest, then up to ceiling, then stretched out the opposite direction of your toes.
As for the basic swing on high bar, focus on hopping the hands and looking down at your toes, sticking your butt behind you in a pike position in the back swing. Your body should be in arch ( for beginners in the hips, beyond that it should be arching through the thorasic area and ribs/shoulders ) underneath the bar and then moving the body back into a pike in the front swing.
Ideally, in both the front and back you should be hollow, but it's fine for beginners to pike.
Here's kind of a beginner example of a swing. She doesn't arch through the bottom as much as I'd prefer but very few L5 girls do.
Wait a tic, are you talking about swingin on high bar or swinging on parallel bars?
If it's pbar swings, most beginner pbar swings pike in the front and arch in the back. Eventually you'll learn how to keep the body stretched in the front ( and even lean back a tad to allow you to swing higher ). Planche slightly forward in the back swing, kicking through the bottom ( eventually you'll learn how to swing hollow which is necessary to not fall out of the handstand ).