Reading this answer that said that ことにする is an idiom, and I began to wonder what the origins of this idiom were. I believe that since the two grammar structures are related, ことになる would also be an idiom if that is the case.
Additionally, it crossed my mind that ことにする and ことに決める have similar usages and meanings, but I haven't heard a conjugation of 決める that would have a similar meaning to ことになる。 If I had to guess, you might have to either use the intransitive form, 決まる、or you might want to say that someone decided that (verb).
So how would I rephrase this sentence using 決める or its intransitive counterpart?
Would it be this?
So to sum up my questions shortly:
1) What are the origins for the idioms ことにする and ことになる？
2) Can I replace the ことになる grammar with the 決める verb or its intransitive counterpart?