"It is beginning!"
No, "on" = "he" and not "it". And "He is beginning" is a pretty strange sentence on its own.
Grammatically, it could be "ono", but that's totally strange, "to" is more possible... but frankly, to me the only really natural answer is just "Zaczyna się". English must use "it", but with such a sentence, obviously it has to be known from the context what "it" is.
EDIT: And now I see that "on" and "ona" are actually accepted... I really think they should not be, that sounds absurd.
The sentence is weird but so are many sentences here. It sounds strange with "on". "Zaczyna się" makes sense. Thank you, Jellei :)
No, it shouldn't. This sentence just doesn't make any sense without a context (you have to know what 'it' is), so it also doesn't make any sense to use "to" as you will know the context.
I don't think you can. I mean, literally "Dzieje się!", but that doesn't make much sense, unless you make it at least "To już się dzieje/To już ma miejsce" (It already is happening/going on, It already takes place).
Maybe "Zaczęło się!" (It has begun!)?