It isn't a codeshare arrangement, but it is an interlining agreement. Baggage should be transfered automatically for you.

Depending on the farecodes, you could put the MAN -> LHR and LHR -> MAN segments on your BAEC account. but you might need to retroclaim this as you might not be able to put your BAEC number through the Korean Air booking. Everything I've seen suggests this will work fine.

You won't get anything BAEC related for the long haul segments though.