is it possible to connect 18 bipolar NPN transistors of type BD135 simultaneously on an Arduino Mega?
If each gets a base current of approx. 11mA, then that would be a total of just 200mA.
Is this feasible if I supply the board via 5V USB?
I can't say no because I've not done much with a mega but you are pushing the limits of the board. I couldn't find an exact spec in the ATmega2560 datasheet but they did state the absolute max current draw was 200 ma.
You didn't state your load but for switching usage the rule of thumb is to have Ib = 1/10 of Ic.
If you are not committed to the BD135 I would look for a MosFet to replace the NPN. Mosfets take little drive current from the processor, like in the micro amps.
Yes it depends on your circuit configuration. Post a schematic, not a frizzy picture with links to the hardware devices. Also take a look as suggested by John Robb, MOSFETs would probably be a better choice but without a schematic that is just a guess. Where did you come up with the 11mA base current?
But I can safely say that the IRF520 modules do their job perfectly. I was able to do a test run yesterday and the transistors didn't even get hand-warm. That means for me that Vgs is sufficiently and therefore absolutely suitable.