Recently I have tried to become more proficient in writing emails in Chinese. The structure for these are difficult, I have provided an example of a email I recently wrote. Is this correct grammatically and structurally?
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There are some basic grammatical things you should take note of, along with some stylistic/cultural things you need to keep in mind, considering that you are writing to a teacher, and not a peer. Furthermore, letters are a unique class of literature in most languages, including Chinese. There are specific formats, traditions, and phrases that are unique to letters. In the modern setting, some apply to emails as well, while some are considered a bit archaic. Your command of the balance between modern and traditional will grow as you write and receive more and more letters. I've written some notes sentence by sentence below.
張博士晚上好 -- This sounds a bit Western to me, which isn't necessarily bad, because many native speakers are also influenced by Western phrases these days. In more traditional spheres, the opening to a letter usually follows the formula: 稱謂＋提稱。稱謂 basically means a name, in this case it's just 張博士。 提稱 literally means "elevating phrase." There's a whole list of these things--I've attached a helpful guide below in case you're interested. For a teacher, an appropriate 提稱 is 尊鑑 or 台鑒。 They literally translate to something like "Please view, your dignity." This opening phrase is ALWAYS followed by a :, and nothing else.
希望你一切都好。 The second line is always on the second line and indented. Also, when referring to someone who is higher than you in social class--in this case, to a teacher-- always use the more polite 您。There's not much else wrong with this sentence, except that if you want to be a bit fancier, you could add a 啟辭, literally "opening phrase." Some suitable ones include 「謹啟者」。
我已經學習七張紙你給我。Grammar--take note of the modifying clause here, 「你給我」。This is directly modifying the noun clause 「七張紙」。Modifying clauses come before the noun in Chinese, and is linked with the word 「的」。You seem to have gotten it in the next sentence, so I imagine this was more of a careless mistake. Additionally, the word for study guides, which I'm assuming the 紙 are, is 「講義」or 「學習單」。As to the verb--已經 is paired with Verb+了 to denote tense. And finally, use 您。This gives us: 「我已經學習了您給我的七張講義。」
明天我也要提交ＬＴＴ1。 I don't really understand the context here, so it's hard to say whether or not this sentence should be changed. One thing to note, though, is saying 「明天我也要」implies a connotation of you either really looking forward to submitting LTT1, or you being forced to do so. Chinese contexts get crazy sometimes and this is a good example.
除了你發送的兩封電子郵件之外，還有什麼我應該學習的？ This may be just me, but it sounds a just a tiny tiny wee bit demanding. In Chinese, just a bit more polite fanfare is often a good idea. Other than the usual 您 instead of 你，there's something you can make even more polite for the second part. A more polite sentence could be 「不知道還有沒有其他我應該學習的講義/重點/內容？」
謝謝你的幫助。 - 您
6.你的學生。 In Chinese letters, we don't use the last sentence to describe ourselves. Usually the last line is used to express some polite sentiments to the receiver, such as gratitude, love, care, etc.. This is highly formulaic and you should always consult a guide before you write this. Some gratitude lines include: 「多勞費心，銘感不已」, which means "I have endless thanks for your worries and inconvenience," or 「至盼即時示下,無任感禱」, literally "I very much look forward to your guidance, and am very thankful."
7.歐陽威利 - Following the letter, it is customary to write the word 「緘」 to mark the ending of the letter. In a letter that doesn't have any strong emotions, just the one word is fine. However, if you wish to express more, such as in a case of respect, you may write 「謹緘」, literally "I close this letter with much care".
Some extra info: In Chinese, there's something called 「抬」, which literally means lifting up, or elevation. It is used when you mention a respected person's name within the body (i.e., not the opening or the ending) of the letter. This applies to basically all writings, including novels, official documents, plaques, and of course letters.
There are many kinds of 抬，and there are two that are the most common: 「平抬」and 「挪抬」。平抬 is when you put the respected name in the next line. For instance:
As you can see, breaking the line every time this happens can get quite a bit clunky, especially in official emails that involve a lot of people. Thus, people invented a compromise, i.e. 挪抬. This means just adding a full space before the respected name.
博士晚上好。學生聽聞 王安娜博士近日發表論文，昨日拜讀，奈學生愚鈍有諸多不解之處，特書此請教 張博士高見。
The full edited letter would read:
多勞費心 歐陽威利 謹緘
If the designated person is a professor of a higher education institute, he/she should be called 教授， not 博士。 But you should ask around, since the title is depends on the campus culture.
One can use study 学习 in the class during lecturing, but you will use 复习, 温习, 做笔记 （study the note) afterwards, or even 做完了功课。 我已经复习了您的讲义。 Anyway, there is no need to say you need to submit the homework, unless you are going to postpone the submission.
有什么我应该学习的 is not wrong, but it sound a lot like in cultural revolution society. You can ask : 可否介绍这方面的书本/著作做延展学习。
As this is email, it will be a excessive and nuisance if you use too much "polite verb". It is no harm to ask the professor/lecturer about the communication format. (IMHO, the formality suggested by @user19706 are pretty "entertaining")