Am I being exploited by my supervisor?

Yes you are.

Point 4 is downright abuse of power. You are not in any way obliged to provide free tuition to your advisor’s child! If your institution has reasonable management, you reporting this would result in severe disciplinary action (I think I would have my tenure clock pushed and have something on my record for something like this). Even if you were paid to do it I’d feel weird about having my students tutoring my kids. Depending on where you are on the planet, not getting paid for tutoring is illegal. Your advisor would be in serious legal trouble if you are in, say, the US or Europe.

Drafting emails seems like an odd practice. It’s abusing power to some extent but if the emails are relevant to your work it might be construed as acceptable by some department heads. That said, you’re a student, not a personal assistant, seems like a waste of your time.

You should not be reading and correcting others' work with no credit, this is the advisor’s job. I would be upset if I were the one of the students who didn’t get their advisor’s feedback!

Being an ass about authorship is another bad sign, though in itself may not be too bad. Disagreements about authorship do occur, though the response you describe seems wildly disproportionate. Getting students to the point where they have to 'beg' for your forgiveness is never okay. His job as an advisor is to educate, teach and advise - you are not his pawn or slave.

Taken together, what you’re describing is a toxic and abusive relationship.

What you can do depends on where you are in the world and your department. Most reasonable universities have ombudspersons or student support centers whose job is to help people in your situation. If no such thing exists you can try to approach your department head or dean.

You need to have clear-cut evidence. Emails, records of your visits to tutor the advisor’s kids, written proof that you corrected the thesis of others (say, an email exchange, files sent to you with request for correction, or any other acknowledgement) etc.

I’m sorry you’re in this situation, hope you get things settled. The tone of your post does not make it sound like you are in severe emotional distress, but of course it's impossible to tell. Make sure you get emotional support through what is undoubtedly a rough experience. You do not deserve this, and you should not feel like this is normal.

Obviously, as other answers indicate, yes, your supervisor is exploiting you - plain and simple. But here's a suggestion regarding what you should do about it:

1. Collect evidence on how you've been exploited/abused:

   • Emails
   • Letters
   • Written documents indicating what you are required to do, but also what you're doing (e.g. if your supervisor's daughter writes you some note)
   • Screenshots of text message exchanges in which you're given instructions / requests to perform these activities or which otherwise acknowledge them.
   • Maybe some audio recordings - if you're discreet about it and if that is legal in the state you're in - of your supervisor making inappropriate demands/requests.

   The idea is not to have lots and lots of these, but enough to be able to establish it is actually happening in case he denies it; also, a few choice pieces of evidence you can use to illustrate to people how serious this is when you're talking to them, if it's necessary. Recordings are "just in case", not-use-unless-absolutely-necessary type of evidence though.

2. I don't know what the organizational situation is in SE Asian universities, but consult - discreetly initially - with:

   • Your junior researchers' union representative - if you're unionized.
   • Your graduate student union - if you at least have a union as students rather than employees.
   • Colleagues you can trust and who can attest to your supervisor's behavior
   • (more risky) members of faculty you can trust; they may be biased against you acting against a Professor, but on the other hand may have effective suggestions for you.

   Avoid discussing this matter with people you think would just rat you out to your supervisor.

3. Based on the advice you got, do one or more of the following:

   • Lodge a disciplinary complaint against him, or have your union do so in your stead.
   • (If you're not yet close to concluding your research,) Demand a change of supervisors (better if you have an alternative one lined up) due to abuse.
   • Have your union threaten your supervisor with action against him if he doesn't change his attitude towards you - disciplinary, legal, public-relations, or other collective disruption.
   • Get a story in the press (in-university or out-of-university).
   • Talk to the head of the department/faculty about the situation - preferably not alone but accompanied by supporting-witness colleagues and/or your union representative.

Note: Some of these actions are potentially dangerous, especially if you don't have some colleagues who would speak in your favor, and if your supervisor can get other grad students to deny your claims. So - I'm not recommending anything specific; it depends on the circumstances, the advice you get and the support you have. That being said you should do something, because just laying low and getting your doctoral work done with will mean that your supervisor will find some other poor PhD candidate to lord over.

Yes, definitely he is using you. Let's break it down one by one.

Point 1: Drafting professors' email is a thing that many Ph.D. students do occasionally. But requiring the student to stop doing the experiment in favor of drafting a personal email is not something a good supervisor does.

Point 2: Can be a legit point. Although doing it all the time is tiresome and time-consuming, the professor can get some benefit of doubt there.

Point 3: It's saddening to even hear that. If you help write a scientific paper (even partially), your name should be in it. Let alone professionalism, this is common courtesy. Your professor is not doing that, and is instead getting furious with you which is much worse than being unprofessional.

Point 4: It's not your job at all. He is abusing you. If you do it happily in your spare time, that's another matter.

And yes, by any yardstick, he is using you.