It is hard to remove emotion from your work but you must do it. I have learnt to simply not care if a student doesn't do their work. It is up to them to work, it isn't up to the teacher to beg the student to study hard and enjoy lessons. And if you have people saying Oh we would prefer a female or male teacher instead of what we have now you can't get angry. You just have to realise there are very stupid people out there

You never have to thank students for the opportunity to teach them, but you can of course express your excitement in their potential.
Age does have a lot to do with the respect you will command in your teaching. If you are 17 you hardly have much teaching experience. This isn't to say that a young teacher is bad. You can tell a bad teacher by one that teaches completely from a book and who cannot work with individual student problems, who cannot get into the students heads and realise what is stopping them from memorising a line or playing a line correctly. One who cannot act as a source of inspiration and encouragement and a huge % of teachers are very negative.
I started teaching when I was 18 and I was extremely confident in my approach. Even though teaching piano was totally new to me I had some ideas what to do, I had a lot of experience teaching myself, I knew what worked for me and why, so I tried to mutate my way for other peoples way, all based on my own playing experience. Of course as the years go by you develop and get better, but there is something about student/teacher relationships which is much better when you are younger as opposed to an old experienced teacher.
I remember many students parents with a worried look that perhaps I am a fake and not a real teacher, so then I blast them away with a piano solo and sight read all the music the might have tried to play and play them all perfectly. You show them you are a musical acrobat at the keyboard they forget about your age pretty fast.
Old experienced teachers tend to simply teach and not learn themselevs. That means they simply transfer knowledge to a student and not worry about learning about the student themselves. A young teacher is learning as much if not more than their student while they run their lessons. This learning environment can be very comfortable for beginners (both teacher and student) to develop in.
Because simple issues are not simple for both of you, it is not simple for you to express how to do basic piano procedure because you havent had the experience to teach it, and your beginner student strive to absorb basic concepts. An older teacher can sometimes get impatient and simply leave students to their own devices where starting out teachers tend to cover all grounds making sure everything is right because they are themselves studying how to teach.
It is true that an advanced piano student should not look for a young teacher because there are issues in advanced piano teaching that the young teacher might never have considered, and it is certainly stuff not found in books but through experience. But I find it pretty arrogant when a beginner student would think that a young starting out teacher is not good enough for them. I assure you, going with the top professor in the top music school in the world will do you no good if you are a beginner and cannot take advantage of the in depth knowledge of the teacher. You might as well pay 15$ an hour with some mediocre teacher and learn the basics, then move on.
So if you get annoyed with people you can state this fact, you know your child is still a beginner, they are not a professional musician seeking to fine tune their pianio technique. The basics can be learn from anyone. I tell all my beginner students you know if you have me or someone else there is little difference when it comes to the basics. I guess how I conduct my lessons are very relaxed, we might talk about pokemon cards for 5 minutes before we even play piano!! eheh
I don't know why this came into my head, but smiling is perhaps the single most important things you have to do when teaching anyone anything. People are usually quite shy about what they do not know, they feel inferior if things which you demonstrate so simply are hard for them. You should always offer support and kindness. Make sure they know you are there to help them, make sure they know you enjoy their mistakes and enjoy working on it with them together. We have to be careful not to discriminate ourselves, making students feel inferior because they cannot do something.