Is there a difference between them? And for the verb forms, 答える　and 回答する?

Your verb forms are correct and the difference between them is that 答え is a native Japanese word and 回答 comes from Chinese.

While they essentially mean the same thing, Sino-Japanese vocabulary is generally considered more formal than native Japanese vocabulary and so they appear more often in writing and formal speech. Whereas the native Japanese vocabulary is found more often in everyday speech.


See
http://en.wikipedia.org/wiki/Yamato_kotoba
http://en.wikipedia.org/wiki/Sino-Japanese_vocabulary

Very informative, thanks!