TBH, I am a little perplexed by what appears to be the sudden popularity of the question-ending 「の」 among Japanese-learners in the last several years. I am perplexed because it is used incorrectly or in an unnatural way at least 60-70% of the time by them.
While one could claim that 「神を信じるの？」 and 「神を信じますか？」 have the same surface meaning, the intended nuances would be quite different if said by native speakers. Those two sentences would not be interchangeable in real life by our standards.
「神を信じますか？」 is plain and simple. It means "Do you believe in God?" with no nuance intended. The speaker does not expect a particular answer.
「神を信じるの？」 is not plain in that the speaker already sort of expects a nagative answer. Someone who strongly believes in God himself would NOT say this.
OP is correct regarding the informality of the 「の」.