I think it depends the extent to which these things happen. I can't stand spoilt kids who have their parents do everything for them.
When I was doing my exams, I was really proactive and did lots of work, so my parents never had to "nag" me whatsoever to do it. However, I live with my boyfriend and his 15yo son now, and he wouldn't do anything at all unless prompted. He never takes responsibility for his own work, so we have to tell him to revise - and yes, it does sometimes end in shouting, because we're worried for what his future will hold if he carries on the way he is. It's not like we're asking anything unreasonable. He's capable, but lazy.
With regards to chores, I don't think it's unreasonable to expect young people to do chores. Going back to my partner's son, when I first moved in he did absolutely nothing and was spoilt by everyone around him. I put my foot down and said I wasn't doing everything, but even now he doesn't do very much. He does the washing up after I've cooked a meal, and I've asked him to keep his room tidy and put his things in the washing basket etc - but that doesn't always happen. That's ALL he has to do in his life as well as revise, and he says the pressure is too much for him. God help him in the adult world, or even at sixth form, that's all I can say.
I agree with the third point, that your parents shouldn't mock you or call you names. There's a difference between playful banter and outright bullying, and you should be able to tell the difference pretty easily.
I do happen to agree that MH is treated in the wrong way at the moment. I think everyone is becoming SO aware of it that it's being overdiagnosed left right and centre, which means that those who really suffer sometimes don't get the help they need, or people just think they have a common, non-serious condition, which often isn't true.
For example, I know a few people who got diagnosed with anxiety disorders because of finals at uni. No. If you're not anxious about finals there's something wrong, and if the anxiety is specific to those exams, and goes away after, it's not a disorder.. it's normal, situational anxiety.
The same way that people get diagnosed with depression when they're grieving or going through a hard time. EVERYONE has to go through hard times, not all of those people are mentally ill. You can be sad without being depressed. You can be anxious without having anxiety. Of course there's a stage during grief when things should start to get better, and there's no doubt that grief can TRIGGER mental disorders, but over diagnosis is a really big problem at the moment, and it trivialises issues for those who are genuinely struggling.