How to gain your parents trust, as in they'd trust you to be okay if you went out to a party or to Hang out with friends for the day.
This is a very good question, I might reanswer it in a video but the best way to gain their trust is to show them that you are responsible, considerate and open with them about what you want to do. Try helping out around the house more, try telling them what you're doing with your friends or how late you'll be out to. Anything you can do to show them that there's an open flow of communication will get them to realize that you're handling situations in a very mature way and they will hopefully be more lenient in allowing you to do other things as long as you continue to openly communicate with them.