You might look into the "curly girl" method, don't worry about the name it's just what it started out being called in the 80-90s. It helps people with any texture besides stick straight hair tame the friz. It's been pretty helpful for me to allow my actual curls out without being a puff ball. There's a community driven Google doc that has the concepts and best products. It wouldn't surprise me if you actually have all wavy hair, many people find that once they stop using products that weigh down hair, their hair texture increases.

https://docs.google.com/document/u/0/d/1Q6Dj9WAZxlfBhJSyS5on2rw3-if5cOV3oV-dQ3B0AHA/mobilebasic?pli=1

Some folks iron their hair with a heated electrical device called a straightener. You could try one. I don't think they are expensive. Read all of the directions and be careful. YouTube is maybe useful here, too.

A chemical treatment called a relaxer can also help do what you want, but proceed with great caution. I understand not wanting to pay for hair care. I cut my own as well. But, some things are best left to a pro. Relaxers are alkaline, and chemical burns are easily possible. Some may contain formaldehyde, which is nasty stuff. Long-term use is probably a bad idea, IMHO.

Regarding 2: ever tried paying a non-professional to cut your hair?

There is no natural way to get your hair to stay flattish. If your hair is poofy, it will stay poofy. You can use hair stylers or hair gels to form it the way you want, but that of course won't be permanent and will cause damage in the long run.

Do you use a hairdryer?

I can feel your pain. I have “poofy” hair and I’m trying to grow my hair longer. I switched to Uppercut Easy Hold and it’s helping me get through those awkward times.

10/10 would recommend.

HTH!

My kid with similar hair likes the Verb Ghost Oil. It's too light for me but adds just a hint of weight and smoothness.

My other suggestions to try are salt spray or a light wax, those can help you get the sort of piecey look.

It's also possible that it's curly - often people with hair they think is straight and poofy have curly hair, in which case either rolling with it, styling it like curly hair, or heat styling to straighten it will work better.