I have heard that multilingual people switch their brain when they use another languages. I have heard that multilingual people switch their brain when they use another languages.

Multilingual just refers to being able to speak more than one language. Need to specify people afterwards to make the sentence make sense.

I heard that multilinguals switch their brain when they use another languages. I heard that multilinguals switch their brain when they use another language.

or "multilingual people"

I've heard that multilingual people switch their brains when they use another languages. I've heard that multilingual people switch their brains when they use other languages.

I have studied English linkingbut my native language is Japanese. I have studied English but my native language is Japanese.

I have studied English linkusing Japanese. I have studied English using Japanese.

or "through Japanese"

I have studied English linkusing Japanese. I have studied English using Japanese.

I want to switch my brain, but I lack the English knowledge. I want to switch my brain, but I lack the English knowledge.

I'd use "the" because it's a specific knowledge you need, you don't lack English knowledge in general (your English writing tells me that much!)

I want to switch my brain to English, but I lack Englishthe knowledge needed. I want to switch my brain to English, but I lack the knowledge needed.

Do you have any ideas? Do you have any ideas?

Do you have any ideas? Do you have any ideas?