Obviously,e English is an international language around thein today's world. Obviously, English is an international language in today's world.

(1) "English" is the name of a language, so it's a proper noun and should be capitalised. (2) "Around the world" is redundant, because it's already implied by the word "international". I just replaced it with something else.

Obviously,e English is an international major language around the world. Obviously, English is a major language around the world.

The phrase I think you're looking for is "lingua franca", meaning it's a common language even between people who speak other languages natively.

I'm actually learning this language because it's an quite an essential condition toskill for shapeing my future. I'm actually learning this language because it's quite an essential skill for shaping my future.

Your original phrasing might be okay, but I personally think "for shaping my future" sounds more natural in this context.

I'm actually learning this language because it's an quite essential condition to shapeskill for my future. I'm actually learning this language because it's an essential skill for my future.

So I really need to improve my eEnglish skills. So I really need to improve my English skills.

Alternatively: "Hence I really need to improve my English skills."

So I really need to improve my eEnglish skills. So I really need to improve my English skills.