Teens can be incredibly difficult IME but also incredibly rewarding. They start becoming the personality they are going to be for life. It's up to us to guide them
OK so in reality it can be a massive pain and you'll have weekly occurrences of wanting to push them out of your moving car.
If they have MH issues then speak to everyone possible to get them support - school, GP, CAMHS, private counsellors if necessary.
Pick your battles. Don't sweat over stuff like "messy room" as long as it's not an active health hazard. Do sweat over basic behaviours like speaking respectfully to others.
Give them responsibility for something in the house. "Hey DS, you are really switched on about household security. It would really help me if you could be responsible for checking all the doors and windows are locked at night, and on the whereabouts of everybodies keys."
Spend time with them 1 on 1 as opposed to with all the kids. I know this can be difficult if you have many DC and work full time. But even an hour a week can make a big difference. It could even be useful if you get them to come do the shopping with you!
Every day, try to find 3 things to praise them for.
"You look really smart today!"
"Thanks for tidying up the sitting room before I got home, it really makes my day easier."
"It sounds like you were a good friend/student/whatever today, I'm proud of you."
Important note - I have never praised innate qualities like "beauty" or "cleverness". It can be divisive to siblings and can cause the child anxiety - what if I have an accident and then I'm not pretty? Always praise the effort that your child has made. Because that's something that they've done, not that they've been.