I am looking at a business class multicity ticket LHR-ICN-KIX and NRT-ICN-LHR for May/June holiday and my dates are inflexible because of work. KE is giving some really suitable departure and arrival times for me. However, the two transit durations in ICN are short (particularly the first one):

KE908 LHR 19:35 - ICN 14:35+1
KE725 ICN 15:20 - KIX 17:10 (45 minutes transit time)

KE706 NRT 09:15 - ICN 11:45
KE907 ICN 13:30 - LHR 17:25 (1 hour 45 minutes transit time)

Is the outbound transit possible? Maybe I can run between gates but will my luggage catch up? If delays occur does KE ICN ground staff assist business class passangers catch their connections or just leave them and re-book on to the next available flight? I have not been to ICN since the new Terminal 2 opened.

Thanks