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My name is Lily and this year I'll turn 30.

I think "this year I'll turn 30" is grammatically correct. In day-to-day speech we can say:
"this year I turn 30"
"this year I'll be 30"

After more than 10 years working as an accountant, now a adays I feel like I don't want to work as accountantone anymore, and I don't know what to do.

I would say:
"After more than 10 years as an accountant, lately I just don't feel like doing it anymore and I'm not sure what to do."

All of my background is in finance, so now iit's pretty difficult for me to change, and. I don't know if I'm ready for that, but, at the same time, I know I'm not happy anymore with numbers anymore.

"All my background is in ..." is fine in speech and sounds natural.

Also, I have to say, that I'm from a little city near Barcelona, and now I'm, living in Barcelona and tha, it makes me feel thatlike I want to change a lot of thinkgs in my life,; for example: my professional career, or where I work.

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I feel thatlike I don't want to work for a national company...

I want to talspeak English, have an international environment atin the office, and meet different people, from different countries... this iThat's why I'm doing this... ¶
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My problem with English is that i can understand everything, but when I have to talk, or to write, I don't know how to do it.

After more than 10 years working as an accountant, now a adays I feel like I don't want to work as accountant anymore, and I don't know what to do.

"nowadays" is one word. added "like" before I don't want to...

All my background is in finance, so now it is pretty difficult for me to change, and I don't know if I'm ready for that, but at the same time I know I'm not happy anymore with numbers.

added "it" before is pretty difficult. you need a subject here. "it" is the subject, being your job as an accountant.

Also I have to say that I'm from a little city near Barcelona, and now I'm living in Barcelona and that makes me feel that I want to change a lot of thinkgs in my life, f. For example, my professional career, or where I work.

changed "thinks" to "things." Made "for example..." a new sentence and added a comma afterwards to show a pause and took away the comma between "professional career" and "or where I work."

I want to talk in English, have an international environment at an office, meet different people, from different countries... this is why I'm doing this... ¶
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My problem with English is that iI can understand everything, but when I have to talk, or to write, I don't know how to do it.

Added "in" to make it "talk in English." changed "a" to "an." Added "an" to "at office." took away the comma between "meet different people" and "from different countries." made the "I" capital. took away the comma between "to talk" and "write." took away to "to" in "to write." added a comma after write to show a pause in thinking or reading.

Crisis in my 30's

After more than 10 years working as an accountant, now a adays I feel like I don't want to work as accountant anymore, and I don't know what to do.

"nowadays" is a single word, not a phrase.

All my background is in finance, so now it is pretty difficult for me to change, and I don't know if I'm ready for that, but at the same time I know I'm not happy anymore with numbers.

Also I have to say that I'm from a little city near Barcelona, and now I'm living in Barcelona and that makes me feel thatlike I want to change a lot of thinkgs in my life, for example my professional career, or where I work.

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I feel that I don't want to work for a nationaldomestic company...

We'd normally say "domestic" company when comparing against companies from other countries.

A "national" company would be used when comparing against a "local" company (e.g. one that's in all of Spain vs one that's just in Barcelona).

Meaning wise, it's clear and logically valid, but they're just not the words that natives would pick so this is a pretty nitpicky correction.

I want to talk English, have an international environment at the office, meet different people, from different countries... this is why I'm doing this... ¶
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My problem with English is that iI can understand everything, but when I have to talk, or to write, I don't know how to do it.

"an" is used for words starting with vowel sounds ("international" in this case)

Crisis in mMy 30's

In title case, basically everything but articles, prepositions, and some conjunctions should be capitalized. You could also say "Thirties." I found this on a quick internet search:

Which words should not be capitalized in a title?

Articles: a, an, & the.
Coordinate conjunctions: for, and, nor, but, or, yet & so (FANBOYS).
Prepositions, such as at, around, by, after, along, for, from, of, on, to, with & without. (According to the Chicago Manual of Style, all prepositions should be uncapitalized in a title. NIVA and I recommend capitalizing prepositions 5+ letters long).

Which words should be capitalized in a title?

The first and last words should always be capitalized, even if they’re in the above list.
All nouns, pronouns, adjectives, verbs and adverbs should be capitalized.
Subordinate conjunctions, such as after, as, because, how, who, if, than, what, why, that, when, where, whether & while.
Commonly missed words: it (pronoun), is (verb), be (verb) and their/our/my (adjective) should all be capitalized.

After more than 10 years working as an accountant, now a adays I feel I don't want to work as accountant anymore, and I don't know what to do.

You may also consider substituting "but" where it says "and."

All my background is in finance, so now it is pretty difficult for me to change, and. I don't know if I'm ready for that, but at the same time I know I'm not happy anymore with numbers.

It would be more natural to break this up into at least two sentences. Above is only one way, but not the only way. For one more example, you could say:

All my background is in finance, so now it is pretty difficult for me to change, and I don't know if I'm ready for that. At the same time, I know I'm not happy anymore with numbers.

Also, I have to say that I'm from a little city near Barcelona, and now I'm living in Barcelona and that, which makes me feel that I want to change a lot of thinkgs in my life, for exampllike my professional career, or where I work.

"like" would be a bit more natural to use in this case. Also, "which" is a more concise way to say "and that."

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I feel that I don't want to work for a national company...

I'm not quite sure I understand the use of the ellipsis here, but I think it can be removed.

I want to talspeak English, have a international environment at the office, and meet different people, from different countries... this, which is why I'm doing this... ¶
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My problem with English is that iI can understand everything, but when I have to talk, or to write, I don't know how to do it.

We either usually say "talk in English" or "speak English."

Also, since you already had "to talk," the verb for "to write" doesn't need to have the "to" anymore. Another example:

"The dog loves to bark, to run, and to play." would be better as "The dog loves to bark, run, and play."

But if there are only two things, there doesn't need to be a comma. Another example:

"The child wanted to draw or read."

Thank you,.

If you were signing off like on a letter, you could say

Thank you,
[your name]

but if there isn't a name at the end, then just "Thank you." or "Thank you!" is appropriate.

After more than 10 years working as an accountant, now a adays I feel like I don't want to work as an accountant anymore, and I don't know what to do.

All my background is in finance, so now it is pretty difficult for me to change, and I don't know if I'm ready for that, but at the same time, I know I'm not happy anymore with numbers.

Also, I have to say that I'm from a little city near Barcelona, and now I'm living in Barcelona and that, which makes me feel thatlike I want to change a lot of thinkgs in my life, f. For example, my professional career, or where I work.

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I feel that I don'tlike I want to work for a n international company...

Usually company is considered “national” otherwise you’d say “international company”

I want to talk English, have a international environment at office, meet different people, from different countries... this is why I'm doing this... ¶
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My problem with English is that i can understand everything, but when I have to talk, or to write I don't know how to do it.