In my opinion, this may be best approached as a sequence tagging problem, similar to part-of-speech tagging or named entity recognition. (So, this would be the seq2seq option, rather than regular classification). For example, think about it as trying to decide for each token, whether it is the start of a new verse or not.
The advantage of the sequence ...
That's a tough one. I don't know what could cause that.
It can be hard to know why we see the results we do, when working with neural nets. Often the best we can do is form several hypotheses, and then devise experiments to try to test those hypotheses.
Some possible explanations that you could try to test:
Perhaps it is noise / random chance
Perhaps the ...
No, there are no guarantees. SGD finds a local optimum but not a global optimum, and the solution it finds can be arbitrarily bad, if you have an unfriendly objective function.
The only results I've seen that provide guarantees start from strong assumptions about the objective function (e.g., convexity).