This is what I think:
Is the following sentences grammaticaly correct?
I can't learn foreign languages quckly. Or It has to be written like " I don't learn foreign languages quickly.
To me both these sentences sound odd. I'd say 'I'm not good at learning foreign languages.
She had an accident. She is gradually improving. (1)
She had an accident. that's whay she is walking slowly. (2)
Please explain why Not "she is improving gradually" and she is slowly walking?
(1) Because by doing so you'd be laying unreasonable emphasis on the adverb (gradually, not quickly). While the focus of the sentence is 'improving', as opposed to worsening.
(2) Here it's the opposite situation. The focus is 'slowly' (not quickly, because she hasn't fully recovered yet). If you put 'walking' at the end, then the meaning would be that 'she is slowly walking, not running, which is ridiculous.
Student or Learner