Weight Questions...

I have a 3500 Dodge with a 40' flatbed..
The trailer tag says 25,900 on it for a GVWR
It has 3 dual axles. The tag says the axles are 8633 GAWR ea. the guy I bought it from said they were 12k axles...??

My truck says 12,2 in the door jamb and 5200 GAWR Front and 9350 GAWR Rear..

I am putting a flatbed on it and want to register it for it's max..

Is that max 38,100 lbs? And does this combination give me a total payload capacity of 21,120 lbs since the truck and trailer scaled at 16980?

Do I need a Class A to drive this setup if not commercial?

If the axles are 12k axles, can the trailer be registered to carry 36k even if the sticker says 25,900?

Thanks for your help.. Should I post this somewhere else?