I've just bought Tamiya's tank transporter FAMO & Sd.Ah.and I'm wondering if my idea of it's load is correct. I want to put on the trailor an early T-34/76 tank which was found somewhere in Russia during operation Barbarossa. Let's say, that the guys from the Famo crew found this tank stuck in the mud and they decided to pull it out. Good idea?
I don't want to use a typical german panzer tank because it seems boring to me.

That's a bully idea. There is also a famous photo of a captured KV-2 tank the Germans took back as a prize. I bet Frenchy knows the one I mean.

Basically there are 2 problems:
1. Would this be possible in the real life?
2. Is the T-34/76 not to heavy for Famo trailor?

Even if it was beyond the typical load rating from the factory, in time of war, especially early on, the Germans were probably pretty excited to get to see a T-34 up close and bring it back for testing. They didn't tow the thing back to Berlin with it, but they certainly could have moved it back to the nearest train yard. I say go for it.