Are my understandings correct?
A. I have been to Korea for two months. Does it mean I have this experience and have been there at least once(showing experience)
B. I have been in Korea for two months. Does it mean I went there two months ago and I am still in Japan now.(something started in the past ans has continued up to now)
C. I am what I am vs I am who I am. What's the difference in meaning? ?
"I have been travelling to Korea for two months" would normally be said only if you are two months into a rather long journey.
"I have been in Korea for two months" can mean that you have just returned from Korea after a two-month stay or that you are still there, two months after you arrived. Context will make the meaning clear.
"I have been to Korea for two months"
For your meaning, I would use "in".
"I have been travelling to Korea for two months"
For me that would mean travelling there repeatedly over a 2 month period.
(B, on the other hand, would normally imply that I am still in Korea, having arrived there two months ago.)
'In' is fine. It's just that 'to' is possible.