Hello seasoned travellers and i apologise for the wall of text!
Hoping we can get help with a few questions.
We have a flight coming up next week with KLM/China Airlines from Ams- Hkg- Tpe flying on J class.
We booked the ticket through KLM on the phone, with the entire journey on the same booking.
We were told later that we may need to pick up the luggage in Hong Kong and recheck it in, if the airport is not able to tag the luggage all the way to Taipei.

We have about 2 hours from arrival to the next flight's departure.
1. Is it normal for the luggage not to be sent all the way to Taipei? The first leg is a Klm and the second is China-Airlines (not a KLxxxx but a Clxxx). I found it strange as the ticket were booked by a KLM agent on the phone and the flights are on a same booking.
2. Is 2 hours enough time just in case we need to pickup, go through customs/immigration and re-checkin etc? I know we are cutting it thin here. We are flying J class if that helps.
3. Is there a simpler way to do this without going through immi/customs?- for example a transfer desk in arrivals where they can redirect the luggage?

Many thanks!