Rule 1 isn't a "good idea", it isn't a "guideline", it is a fundamental tenet of transistor physics. If for any reason (during normal usage) it is unable to hold then the circuit will not operate.
As for the lamp, it is a purely resistive element. It should have 10V across it, but thanks to the transistor it won't. So the transistor gets 0.2V and the lamp gets 9.8V and reality is saved.
First, you mix voltage and current. Voltage is the "pressure" on electrical charges, so they want to move. Current is the flow of electrical charges, if the find a way.
Case 1:
To answer the question, have a look into this datasheet of a common BC337
The table on page 2 states a Collector Cutoff Current of 100nA for V_CE=45V and V_BE=0V.
So yes, there will be a current through the collector. Keep in mind that a NPN transistor looks like two diodes connected back to back:
simulate this circuit – Schematic created using CircuitLab
While this doesn't describe a transistor in general, here it does. You are operating the upper diode in reverse direction. In this case, real diodes will show a small leakage current, 100nA is a perfect sample for it.
You didn't say where E should be connected to, but if it's connected to GND, as in my schematic, the lower diode is shorted by the connection between B and GND, so the 100nA will flow through the base leg. It's just the same as if E is not connected anywhere. If E is also connected to Vcc, you just get a second diode in parallel to the first, so about twice the current (depending of the characteristics of the diodes)
Case 2
Well, if only B is connected to Vcc, and the rest is not connected to anything, no current will flow. If you connect E and/or C to GND, the diodes will be operated in forward direction, and a significant current will flow (and destroy the transistor if currents are niot limited by resistors)
Best Answer
Here's a typical commonly used BJT data sheet: -
If you ground the base (i.e. connect it to 0 volts) then the collector voltage maximum (repeat maximum) voltage is 60 volts (irrespective of current being passed or not). That's what a maximum rating is - it's the point-of-abuse limit. Anything above is abuse and anything closer to 0 volts is not abuse. In truth though, to obtain best reliability you shouldn't really get to within 75% of that maximum limit. And by that I mean around 45 volts. And, I don't mean an average voltage I mean an instantaneous value so, 60 volts for 1 femtosecond or half an hour is equally abusive.