Both mean "again" with shades that make sense in some context and don't make sense in others. СНОВА can be used with an additional shade "anew" (from the beginning). ОПЯТЬ has a connotation of repetition with no significant change. If that's not what you want ("eh? Could you please say that again?"), better reconsider and use "ещё раз" (another time, one more time). Otherwise they can double each other.

It's synonyms. But снова has one more meaning - from the very beginning. (Ему придётся начать снова.) Of course you can say опять in this sentence, but it will be a bit different. You can use interchangeably, you will be understood

I guess the difference is the same as between the words "again" and "anew" - from the very beginning

These words are synonyms, but they have a little difference in the emotional coloring, which only a native speakers can feell:)