Yes, using 'for pleasure' as you did is fine. But it's more 'doing something for pleasure' rather than 'do something for pleasure'. So in your example you should say, 'I'm learning English for pleasure' (not 'learn').

You are correct in using the phrase "for pleasure". This is why when travelers are asked at Customs about the purpose of their visit, they are asked, "Is your trip for business or pleasure?"

Yes, perfect.

Thank you all :)

Absolutely! Spot on:)