They have essentially the same meaning. Reply is a little more formal. So it would depend on who you were replying to/ answering. To a friend you might use 'answer'. To someone you didn't know, you would more usually use 'reply'...

If a realtor contacts you and says ‘There’s a new house for sale and I think you should see it as soon as possible.’ there isn’t a question that can be answered. So the realtor would say ‘Please (reply/let me know what you think).’ There are many meanings of ‘answer’. Your examples suggest that you have/had asked a straightforward question.

Thank you very much