imk is incorrect. it is "I want to learn English to fluency." you can speak fluently, but you can't learn fluently

Yes. For instance, it would be correct to say "I would like to learn English fluently"

I would never say this. It would be better to say 'I would like to learn to speak English fluently'. In this case, fluently modifies the verb 'to speak'. The most common usage of the adverb fluently is to describe the act of speaking a language.