You will have to clear passport control upon leaving the Schengen area in DUS, but you would need to do that even if you had booked it all on one ticket. On the upside, there is of course no passport control nor customs on the domestic TXLDUS leg.
As for checking in, it doesn't hurt to ask, but I don't think they'll be able to. I've never flown with Cathay, can't you check in online?