I've been in a lot of third world airports and English has always been fine for figuring out what to do.

The code numbers you were given are the usual way ticketing works these days--I haven't had a physical ticket in many years. They work fine, you should have a seat although overbooks are still a part of air travel.

Your bags should be checked as far as Inchon. Beyond that it depends on interline agreements and what Korean rules are on clearing Customs. In the US you always reclaim your bags at the first city you land in and clear customs at that point then recheck them. They're tagged to your final destination but they come out on the carousel at the port of entry.

While I've been in plenty of other countries my destination has always been the city I landed in so I don't know what the general pattern is on this.