Opinion is how you feel about a person or thing, as in:
"What's your opinion of country music?" (do you like it or dislike it?)
"What's your opinion of this book?" (was it interesting to read?)
Idea is a mental process, the result of mental activity, thinking, contemplation, as in:
"I have a lot of ideas for inventions." (I've thought of many things that don't exist that I'd like to invent)
"Can you think of any ideas on how to solve this problem?" (This problem has no solution yet, can you think of a plan we could use that might finally solve it?"
(not a teacher, just a language lover)