Maybe random checks, but i often take the train from PL to D and have never had passport checks.
The Polish tend to check in terminal stations like Zgorzelec, Kostrzyn and Szczecin - but they tend to leave true international trains alone like the Berlin-Warszawa-Express. I saw some Chinese people pulled in Szczecin - but they were ignoring anyone with a white face.
Folks, upon exiting German airport, don't you think it would be the same problem because passport will be checked anyways?
I think every day that you bury your head in the sand about the issue makes it more likely that you'll be banned upon leaving. Anyway, yes, you'll have even more problems leaving Germany - they check every passport thoroughly.
Can you extend a tourist visa? That is, apply for another 3 months like with a business visa?
Nup, the only option is to apply for residency - but if you're already over the 90 day limit, that option ceases to be available too. As far as I'm aware, there's no way of legalising yourself if you're already illegal.