모르겠어요

몰라요 is more direct and factual. 모르겠어요 is softer, more polite, and implies a subjective feeling of not knowing.

Yes, but '모르겠습니다' is safer in a very formal office. '모르겠어요' is fine if you have a friendly relationship.

You can say '전혀 모르겠어요' or '하나도 모르겠어요'.

It's a suffix that adds a nuance of 'conjecture' or 'it seems to me', which makes the statement less blunt.

Yes. '그 사람을 모르겠어요' means 'I don't know that person'.

Only if you say it to someone older or a stranger. With close friends, it's perfectly normal.

Use '왜 그런지 모르겠어요'.

Yes, it is often used that way, though '이해가 안 돼요' is more specific to understanding.

모르겠습니다 (Moreugesseumnida).

Yes! '뭘 살지 모르겠어요' (I don't know what to buy) is very common.

No, '모르다' is a pure Korean word.

It's a flap sound, like the 'tt' in 'better'. Don't roll it like a Spanish 'r' or make it heavy like an English 'l'.

In formal writing, '알 수 없다' or '불분명하다' (unclear) is often preferred over the conversational '모르겠어요'.

You can say '몰라요~' with a rising intonation at the end.