I have this transistor 3904. My question is: what is the max voltage I can apply to the base? Is EB voltage it? Why is CB voltage is so high? And why is there any voltage there at all? CE voltage makes sense but CB voltage?

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You had better read up on transistor basics.

To answer your first question, the max voltge you can put on the base is really unlimited. However, when the voltage is sufficiently beyond ~ 0.65V or so, the device could be in saturation and might get destroyed depending on it's power dissipation. so I dont know unless I know the rest of your circuit.

The statement why is CB so high makes no sense. Are you talking about the max value it can have from the datasheet? If so, it is so high because it was designed that way.. ask a more sensible question.