Questions about できる and the potential form

Question

I know that the potential form can take either が or を depending on the volition degree when it comes to godan and ichidan verbs

漢字を読める (high volition) or 漢字が読める (low volition)

My question is regarding the case when there is a noun followed by a 漢語名詞/する動詞. Is it correct to say 英語が勉強できる？ I am asking this because most examples online are using godan verbs like the previous example which I already know. Online, I would probably find a 英語を学べる. I always catch myself using a normal verb because of not being so sure about this grammar point.

I also know that I can use the 名詞＋が＋できる pattern as in 日本語ができる, but does it mean that saying 英語が勉強ができる is grammatically correct?

By the same logic, is it grammatically correct to say 英語を勉強をするのが好き？

I came back to genki 2 after not finding a proper answer on 日本語文法辞典, and they say that using できる with を is a substandard use. That is a ambiguous. Does it mean sometimes people use it? Does it depend on the formality level of the conversation?

I also noticed that everytime I think of saying 名詞＋漢語名詞 in the potential form, I tend to say 名詞＋を+漢語名詞+できる

Example: 英語を勉強できる

Is it a real tendency I absorbed with immersion or is it a language bad habit?

A similar question has already been made but was not answered properly What is the difference between が（suru-verb）できる and を（suru-verb）できる?

Answer 1

Is it correct to say 英語が勉強できる？

Yes. 勉強できる works just like a potential verb 読める here. And here you can use 英語を, too.

is it grammatically correct to say 英語を勉強をするのが好き？

No. You can say 英語を勉強するのが好き (without を).

saying 英語が勉強ができる is grammatically correct?

No. In this case, できる alone is like a potential verb and can take only one Noun+が. In this sense 勉強できる and 勉強ができる are different. The former can take another が-phrase but the latter not (taken already by 勉強が).

So 英語ができる or 勉強ができる is fine, but 英語が勉強が is not.

英語を勉強できる

It is fine. My impression is 英語が勉強できる may be (slightly) more common though it may depend on words as well.