picking up luggage

Hello, Stephan, if you hold an all-through air ticket, then it's possible your luggage will be delivered to the destination. If you hold separate air tickets, you may need to claim your luggage at the transit airport and you’d better contact with the airline to confirm.
Yes, there is luggage storage zone inside the airport to store your luggage for a short period of time. Three places are available for you to store your luggage.
For T1, the left-luggage counters is on the east of Corridor between T1 to T2
For T2, the left-luggage counters are near gate 9 in the arrival hall on the first floor and gate 10 and gate 8 on the departure hall on the second floor.
T3 provides round-the-clock left baggage consignment and packing service at east of public space of Arrival Hall at 2nd floor of T3-C and west of public space of Arrival Hall at 2nd floor of T3-C