[kebisan]

From my experience, 「学習」 is closer to the word "Learning" while 「勉強」 is closer to the word "Studying." For example, you probably will never hear 「明日のテストのために学習しています。」Instead it's more correct to say 「明日のテストのために勉強しています。」But similar to the words "Learning" and "Studying" there is definitely overlap in usage.

The same goes for 「返事」and「答え」There are certainly instances where you can use the words interchangably. But I like to think of「返事」as more of a "Reply" and 「答え」as closer to the word "Answer." To give you an example here, it's correct to say 「手紙の返事はもらいましたか。」 but incorrect to use 「答えましたか」in this case.

Hope this helps a little!!