The MAN-LHR is a BA code, isn't it? And LHR-ICN is a KE code.

So no codesharing is involved here: this looks like a bog-standard interline connection that can be fared using a KE MAN-SEL through fare. There are plenty of these arrangements between airlines that are members of different (or even no) alliances.

It would be written on one ticket, and you'd be contractually entitled to through-checking of bags if there is a baggage interline agreement between BA and KE (which there is).

You can earn Avios for the BA flight, and for the KE flight you can earn in whatever scheme earns for KE flights.