한시에요 -> 1(한)시예요. "A" only means "one o'clock". If you're trying to say "it's 1 o'clock", you need the "is" part. So b) is correct. Yes, either 입니다 or 이에요 is fine. Same word/verb/meaning, just different speech levels. 1시야 is for close friends, children, pets. 1시다 is for your diary or the news. I would focus on the 요 form, not ㅂ니다/습니다 form. It's formal.

Language isn't particluarly gendered in Korean, as with Japanese (where males and females use noticeably different language).

You can also use '한시'. but this is a little rude for a stranger. '한시야' and '한시다' is not divided for woman and man. Every people can use '한시야' and '한시다' regardless of gender.

Thank you for the guidance. As for '한시야' and "한시다', is there specific difference between them, apart from being causal? Or is '한시야' used mostly by girls and "한시다' by boys?

b '한시입니다.'(polite) / '한시야' or '한시다'(friendly)