You asked to correct the whole text. So, my corrections of the whole text are below.
I also capitalized first letters of each sentence, and corrected some punctuation.

Ты изучаешь китайский, а я изучаю русский. (See explanation by maxmixiv above).

Я думаю, что русский трудный, но ... (I think Russian is difficult, but ...) - in this case you need an adjective (трудный), not an adverb (трудно).

Or, if you add a verb, than the adverb is OK (adjectives modify nouns, and adverbs modify verbs):

Я думаю, что русский трудно изучать, но ...
Я думаю, что выучить русский (будет) трудно, но ... ("будет" is optional, but it is implied).
Some other wordings are possible as well.
- See explanation by maxmixiv above.

..., но мне он нравится.
(You cannot use "этот" here, since "этот" means "this" or "this one". When you refer to something mentioned before, just to substitute a noun, you use "он/она/оно/они", just like English "he/she/it/they": I think Russian is difficult, but I like it. In Russian, "язык" (language) is masculine, so you substitute it with "он").

You can use "этот" to modify a noun: ..., но мне нравится этот язык.
Or, when you have an opposition of "тот" and "этот" (that one and this one): тебе нравится тот язык, а мне - этот (you can even omit "нравится" in the second part), but that is not your case.

Я очень рада, что ты говоришь по-русски.

Never say "по-русский", it is wrong. And it is a very common mistake of non-native learners.
In fact, there is an adjective "русский" and an adverb "по-русски".

Я хочу учить русский, потому что я люблю смотреть русские (plural form!) мини серии (actually, we do not say "мини серии", maybe what you mean is "мини-сериалы", but I am not sure).

Я смотрела "Идиот". Я также смотрела "Мастер и Маргарита". - ОК, but we usually decline feminine names, even in titles: Я также смотрела "Мастер и Маргариту" is better.

Конечно, я ничего не понимаю!
Знаешь? Когда я увидела e-mail, я подумала, что я ничего не пойму, но я немного понимаю.
1) When you have consecutive actions, you use perfective verbs to underline this fact: First you saw the e-mail, then you thought ... So, I transformed your verbs to their perfective versions by adding appropriate prefixes (увидела and подумала). Otherwise, it sounds as though your actions were simultaneous (When I was seeing the e-mail, I was thinking...).
2) "I thought I would not understand anything" - that's what you wanted to say, right? If yes, you need a future form of "понимать": пойму.