They mean the same thing, but "yek digar" is more formal and we almost never use it in spoken language (at least in Iran). Although, you can use both one in written language. Cheers.

Hi ! There is no difference between یکدیگر and همدیگر but همدیگر is more common. we use یکدیگر just when we want to write sth importante like an official letter.

They are the same, but همدیگر is more common for colloquial, but we pronounce like this is speaking form /hamdige: همدیگه/ for example: با همدیگر مهربان باشید با همدیگه دوست باشین

Hi There is no difference in their meanings, both of them are used when you want to relate something between two people (like together). for example: those two brothers work together ( آن دو برادر با همدیگر/یکدیگر کار میکنند). To expand the use you can use them to show a relation between more than just two people for example: communities, countries and so on. There is an advice: if you want to sound more native don't use any of همدیگر or یکدیگر both of them are so formal instead use همدیگه which is common form of همدیگر. for example: آن دو برادر با همدیگه کار میکنند.

Hi There is no difference in meaning But we never use 'یکدیگر' when we speak.