It's nice to see you starting the Karl! Here are the answers I can think of:
1) It depends on which kit you got, If it were the Initial kit, ( eight roadwheels, looks like mine) then from what I know you can only finish it in overall grey. The two names were Adam(Nr. I) and Eva (Nr. II). For the barrels, Eva used the 600mm barrel throughout her service life and I think was never repainted (I might be wrong with that point). But Adam used both barrels and I think was repainted. (Still not sure on that one)
If you have the regular kit (11 steel roadwheels) The vehicles were Nr. III (I think it was Odin and used a different track from all the others). Nr. IV, V, and VI were named Thor, Loki, and Ziu. All but Ziu used both barrels. Ziu only used the 600mm barrel. All these I think were photographed and were all in the camo patterns.
As for the Cullenmeyer transports. I'd figure all these would be the same as the mortar it hauled.
Check the instructions, it'll tell you which is which, most likely where you first start the mortar. If not here is were I got all of my info
http://perthmilitarymodelling.com/reviews/vehicles/trumpeter/tr00208.htm http://perthmilitarymodelling.com/reviews/vehicles/trumpeter/tr00209.htm http://geraet040.web.infoseek.co.jp/karl_top-e.html http://jagdtiger.de/index2.htm http://en.wikipedia.org/wiki/Morser_Karl All of these are good sites.
Answer #2, You could always build a shelf!:p
I hoped this has helped. Be prepared for anguish, harsh words and small parts. But in the end you will see the fruits of your labor, a beautiful big boomer that will go anywhere and do anything as it pleases.
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Richard
Currently constructing: Morser Karl Nr. II "Eva" (Trumpeter kit w/ initial and late hulls)