하다 verbs work where you take a noun and combine it with 하다 to mean that you're doing the action for that noun. And they're short for "(noun)를 하다" where the actual verb is nothing other than 하다. Ex: play basketball = 농구를 하다 or 농구하다
With learn (배우다), you don't have that. "배우를 하다" isn't a thing, so 배우하다 makes no sense
That's a different grammar ending ("지" or "지요").
"저는 영어를 배우지?" = "I learn English, right?"
The sentence mean mean or imply anything about lacking the ability to learn.
It simply states that you don't learn.
But it could mean both that you don't learn and that you aren't currently learning, because in real life in Korean the basic present tense is used regularly for the meaning of continuous.