There is so much stuff here that it's very difficult to given an exhaustive, coherent answer. I'll try to split it up into the main topics.
Limiting screen time
It's a pretty well established fact that excessive time spent watching TV and using computers/phones has negative effects on the development of kids, and that these are addictive so that most kids will use them excessively if allowed to.
That being said, a 30 minutes per day limit is quite low, appropriate for small children. Presumably you are a teenager, and you should be generally able to decide what you do with your free time. You'll be an adult pretty soon, and you'll need to self-regulate and avoid addictive things on your own eventually. Maybe this is how you can convince your parents to be more lenient (in this and other things): tell them they need to let you manage your own time and your own tasks to some degree, so you can learn to do that. But trying to bypass restrictions is not the right way to do it.
Depression is serious shit. It can make people kill themselves. You write "sometimes I feel depressed" which some people say when they just temporarily feel sad or hate their life. Those are things that you can do something about (even if it's not easy) and which will eventually pass. But clinical depression has to be treated differently. Read Hyperbole and a Half - that is depression. If that really sounds familiar to you, then you need professional help. Talk to a doctor.
In either case, your dad's reaction ("it's a choice") is absolutely shitty and unhelpful. Sorry for that.
As for "depression is caused by watching TV/youtube", there's a kernel of truth to that, but really only with certain kinds of content (influencers displaying artificially perfect lives, causing body image issues and similar in their folloers), which doesn't sound relevant in your case.
School work and achievements
You parents are right that school is important, math is important, you should finish assignments, and this will probably make your life easier in the future (at minimum it gives you more options). You are wrong to dismiss this for fear of "looking like a nerd".
Where they aren't right is that it's not the only thing that's important. Having a social life is also important - and a basic human need. That as well will make your life easier in the future, social skills are as important as intellectual ones. They are wrong to dismiss your desire to "fit in". And they are wrong to try and force you into extracurricular activities without taking your needs into account.
What you can do about "strict" parents
Your parents clearly think they are doing all this in your best interest, even though some of their methods may be counterproductive. They are focusing too much on superficial goals and too little on preparing you to be an independant person who achieves things for your own benefit rather than because they tell you so.
Your best hope of success is to start an adult conversation where you acknowledge their goals for you, but demand that they also acknowledge your goals and needs. And for that you need to think about what your goals are. If you want them to take you seriously, you have to show them that you're not just complaining about being made to do your school assignments or getting your phone taken away, but that you're ready to take on responsibility for your own life. And then you can talk about what are reasonable expectations on their side what you should do, and on your side how much free time you need to relax and how to spend it.
See also my answer here for a quite similar question: How strict can my parents be about my studying?