supply filtering: read this page.
http://www.muzique.com/lab/hum.htmyour 1k goes between "dot" and "effect 9V" on your dia. "effect 9V" now becomes the clean 9V/supply/Vcc
**. the LED A also goes to "dot", which is the 'dirty DC'. the 220uF cap then goes to the far right, connect (+) to the clean 9V, and the (-) end of the cap to ground.
you need some way of breaking the plus end of the battery connection when the external DC is in-plugged, I'm assuming you know that.
the 47uF does the gain fooling. the 22uF cap does impedance things, bootstrapping the bias point to the emitter to increase the input impedance (I think, I'm always hazy on bootstraps).
AC gain is the diference between the input and the output voltages, yes (before the output begins to clip the signal). [dBV, also, hazy.]
ask your co-worker to find you a 10uF poly cap that he can afford, and that you can fit the build, and yes, fine then replace the electro. we use the electros because they are cheap/small/the correct capacity for the task at hand.
your choice of a high voltage power transistor (2sc3317) as replacement for a small signal audio amplifier is an interesting one. go for your life, mate, it won't break the circuit and it is not dangerous. not much is at 9V. can I ask why, though? can you hear differences?
** you need a new name for each different node, like DC in, supply, +9V. you can't have a point named "9V"
this end of a resistor and
that end of the same resistor.