The source of your confusion is the phrase "at your disposal", which means "this is available to you". The noun itself, however, is a derivative of the verb "dispose", which means "to get rid of", and this noun is usually used with this meaning: the act of getting rid of something.

Overall comment: your vocabulary is quite good but the grammar is lagging behind it. For a more balanced language skill set you should consider studying some more with grammar workbooks (e.g. Murphy or a good reference with exercises written in you native language)

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Apology letters (I would like anyone to correct it. Thanks.)

Ms. Jane Harris,

I was surprised to head hear that you do did not receive (you need to use past tense here) your order placed on 28 August yet. I am so sorry to for (to be sorry for something) inconveniences the inconvenience (inconvenience is pretty much never used in plural) caused by this delay.

I wound like to apologize for have not been not being (as you are describing a state, the -ing form should be used) available last week, I was being in on a business trip. With reference to delay in your order I wound would like to explain that your order has been send sent on time but, the carriage delivery does not depend on me. I has have spoken with the transport company and they said told me that they had lost your box.

Although it is difficult to compensate you for the inconveniences suffered, I would like you to accept a new shipping. I will send your products again in a by express shipping so you will receive your products within 48 hours, also I would like to offer to you by way of compensation 25% off in on your next order.

I would like to apologize again, and can assure you that such situations will not occur in the future, as I have changed the transport company.

Yours sincerely,
Alan Bennet.

Your English is quite good for a foreign speaker and most of my corrections are regarding not mistakes but style. Basically, nitpicking :)

Tsinghua University

Tsinghua University is the best university in China. It's is my honor to study here ('my honor' is a very literary expression that doesn't go very well with the shortened 'it's' This is not strictly a mistake but looks unnatural). The campus here is very big large and beautiful (it is best to use 'large' when you are speaking about a collection of structures occupying a lot of territory. 'Big' is a very specific word you use when talking about singular objects). And what's more important is that the food here is very delicious. There are over ten canteens and each of them are is different from each other (the only real grammar mistake in the text. 'Each of them' is singular, as it is one object). You can eat all kinds of food in Tsinghua, no matter whether it is Western-style food or any kind of Chinese food ('no matter' requires a conjuction, a noun and a verb after it. You can use 'if' or 'whether' as a conjunction but 'whether' is better for written style). Besides In addition ('in addition' is better for a written text, as 'besides' is better for speech but this is not strictly a mitake), you can watch movies and artistic performance, such as opera, ballet, concert and etc. So, living in Tsinghua is very comfortable and I am fortunate ('living' cannot be fortunate but you can).

Оба варианта - очень близкие синонимы, но акценты немного разные: в первом случае акцент делается на "меня нет", то есть отсутствие субъекта (и из-за этого в предложение сложно что-то добавить), во втором - на "не дома", то есть на место. Вполне естественно сказать: "Я сейчас не дома, а в школе", но крайне неестественно будет звучать: "Меня сейчас нет дома, но я есть в школе".

The previous answers are both correct. However, the basic difference is that 'complaint' is an action corresponding to the verb 'complain': you have a complaint when you would like to complain to somebody about something that has affected or affects you negatively. A grievance is a state (which has very little to do with the verb 'grieve' which is mostly used for feelings regarding the loss of a loved one). In other words, complaints need to be brought up in a conversation but grievance is an emotional state towards something that affects you negatively and that you perceieve as wrong and it doesn't require communication with others.

ありがとう、先生、その単語がすごく焼くに立ちます。普通、使いませんが、よく使われる言葉ですから、知っているのは重要です。