The bipolar transistor is a current operated device, the current input to the base is multiplied by the current gain (Hfe). The input current flows from base to emitter and the output current flows from collector to emitter. The base-emitter is a diode. The base voltage increases exponentially with current, reaching a limit at about 0.6 volts for silicon transistors and diodes. For most calculations, you can use 0.5 volts as the base voltage.
The transistor has maximum power and voltage specifications. If you exceed the Vce(max), the transistor will avalanch (become a short circuit) and draw as much current as the circuit resistance will allow. If you exceed the power rating, it will get hot and eventually short out. The power is calculated from: P=Vce*Ic.