I'm resumeding this activity now for professional purposes.

"Resumed" and "now" are incompatible, as the former is in the past tense while the latter implies the present.

So I decided to take a BBC Learning Test to know where I am I right now.

"Where am I" is used in questions. "Where I am" is used in statements such as this one.

I feel quite frustrated because the results showed me that I am still being an intermediate student.

We use "an" instead of "a" before words that start with a vowel consonant.

I thought I could have done anymade some progress at least by listening to eEnglish music, or watching movies or series, or just scrolling eEnglish contents.

(1) The phrase is "make progress".
(2) "English" is the name of a language, so it's a proper noun and always capitalised.
(3) I removed the first "or" because it is redundant and can sound stiff when used repeatedly.
(4) In this context, "content" is an uncountable noun.

The most difficult part for me is the grammar, which seems I could never got learned permanentlyseem to remember.

(1) I tweaked the second half of your sentence so that it's grammatical. It might be useful to memorise this construction: "can never seem to (do something)".
(2) We have a word for "learn permanently"; that is "remember".

Anyway, this is my new attempt to improve my grammar, so I appreciate very deeply your corrections or comments.

"I appreciate very deeply " is grammatical and fine, and may tend slightly towards a more literary tone. Alternatively: "I very deeply appreciate".

So, I decided to take a BBC Learning Test to know where I am Iat right now.

Need the comma after "so" if you're introducing your sentence with it. It can just be "where I am" as well. But haivng 'at' is clearer.

I feel quite frustrated because the results showed me that I am still being an intermediate student.

instead of "being," "am" in the front. Also, when you have "a" in front of a word starting with a vowel (except words starting with u in the way that it's pronounced like w), it needs to be "an."

I thought I could have done anymade progress at least by listen to english music, or watching movies or series, or just scrolling english contents.

The most difficult part for me is the grammar, which seems I could never got learnedlike something I never permanently learnt.

I added "something" because the grammar is the thing you are talking about. If you directly say "which seems like I...," it's like you are describing a situation, but the grammar is not a situation it's an object.

Permanently learnt is just adjective in the front. I deleted could because if you write something like "seems like something I could never permanently learn" is actually talking about the future. This way, you are saying that grammar seems like something you will never permanently learn. So instead, to talk about the past, I removed could.

You could also use "couldn't" instead, but then you need to switch never to ever to remove the double negative you would create. So, something like this: "seems like something I couldn't ever permanently learn."

Anyway, this is my new attempt to improve my grammar, so I deeply appreciate very deeply your corrections or coments.

"deeply" goes in front of appreciate because it's describing the nature of "appreciate"