Electronic – How to `chain` transistors so that the first transistor `switches` on the second

While perusing the IOIO board link provided in the question, I noted that the board has some 5V tolerant open-drain digital output pins. Since the camera has built in pull-ups, as shown in the first diagram in the question, you should be able to connect the open drain pins directly to the camera. You will not even need the external transistors.

The current sink capability of the open-drain outputs is specifed at 20mA, which easily will handle the .5 mA mentioned in the question.

In this case, the camera "expose" and "focus" would be connected to open drain outputs, and the camera ground would be connected to the controller board ground.

edited to add:

I now note that the page you cited in the question, http://www.covingtoninnovations.com/dslr/CanonRelease.html, advises adding an optoisolator to the circuit if the camera will be powered by an AC adapter rather than the camera battery, as shown in the second diagram in the "Serial-Port Cable" section. That is probably a good idea. In that case, you could connect the optoisolator to an output pin on your controller board that is not an open drain pin, selecting a dropping resistor to set an appropriate drive current for the diode.

There are two possible causes of the blown transistors. First, connecting the base directly to 3.7V will cause excessive base current : it makes sense to limit that with a resistor. 20mA is cautious, 100 ohms would allow 30ma which should be safe.

The second in that - while you cannot "push" excessive current like 2A to the motor - if it draws 600mA when running normally, it may draw much higher currents when starting, or when stalled.

Connect the motor to the PSU again, and stall it with your fingers (don't do this with a high power motor! Use some other means of braking it!) Observe the current it draws when stalled ... I'm guessing somewhere over 3 Amps (you may need to fiddle with the current limit to observe this).

It will momentarily draw that current when starting, and that could be fatal to a 650mA rated transistor...