Translation:I am not a middle school student.
I believe David said "なか is its kun'yomi reading, which is generally used when the kanji is used by itself"
Your first two examples are common Japanese surnames hence the kun'yomi (the kanji were matched onto preexisting names), and 真ん中 is typically written with the ん okurigana, which is why both 真 (ま) and 中 (なか) are using their kun'yomi.
High school is 高校 (こうこう), which is an abbreviation of 高等学校 (こうとうがっこう). I'm not entirely sure why it breaks from the pattern of 小学校 and 中学校, but my guess is that it's to avoid ambiguity with homonyms like 高額 (こうがく = "large sum of money"), 工学 (こうがく = "engineering"), or 光学 (こうがく = "optics").
Funny thing, at first I put "high school" instead of middle school because in Hong Kong, 中學 refers to high school since the British educational system is implemented (no middle school). I suppose Japan takes after the American educational system more (primary, middle, high schools)?
If you have been doing the lessons in order (which considering you are level 10 Japanese is highly likely) as you could only do them in order before the upgrade then you would have been introduced to 中 as both ちゅう and なか and also 学 as がく and used in 学校（がっこう). They are both introduced quite early from memory in amongst the very first hiragana lessons. 生 may also have been introduced in those early lessons, I don't recall - but the two I mentioned definitely were introduced early on. So Duo isn't actually throwing unknown kanji at you out of nowhere and expecting you to know them - they were already introduced to you.
"Pupil" is not necessarily incorrect, but as a native English speaker, it doesn't sound natural to use it in this sentence. "Student" is a better fit, and it includes anyone who studies, regardless of their age.
It's hard to put my finger on why though. If I had to try to explain, it's like "student" is the label/title for a person who is studying, but "pupil" is used to refer to a specific person or group of people who are being taught by someone. In this sentence, you are saying that you are not a student, meaning you're not being taught by someone. If you were to say "I'm not his pupil", then you're saying that you are not the specific person who is taught by him. ("I'm not his student" is also a natural and valid sentence, so my advice is to use "student", rather than "pupil", because it's more general.)
Well, you don't have to explicitly write or speak a word(= reference to a person/thing) when the subject is clear.
It is more common for a person to be mentioned, or for one of the expressions of "I" to be used to introduce oneself, if the sentences have negative statements. The simple reason for this is that in normal conversations one does not simply make statements about oneself over several sentences - and then does not have to repeat 'oneself' in negative sentences -, but a negative sentence is often used as a counterpart to a positive statement about another person (=another subject).
- "I am Melanie. I am 30 years old. I am not a student. I am from Germany."
- A: "I am a student. I like to study."
- B: "I am not a student. I also like to study."
- A: "私は学生です。勉強が好きです。"
- B: "私は学生ではありません。勉強も好きです。"
So, if the subject changes, you have to say, who or what you are talking about. If it doesn't, you don't have to repeat it (- maybe, unless you want to emphasize that it stays the subject.)