BJT amplifier modification
I wouldn't hesitate in downloading a free spice simulator and seeing for yourself exactly what happens. LTSpice is quite good and a lot of the major players offer free student-versions of their top product, limited usually in node or component count.

If you're serious about electronics as a hobby or job then, doing what I've said above is more important than getting an answer to your question.

Off the top of my head, it looks to me like it would still work at 5 volts but maybe a tweak to R1 (maybe take it down to 180kohm) might be in order to adjust the bias points of the two transistor. Having said that I still think it stands a good chance of working at 5V.

You can put two speakers in series but the output and input is mono so all you'll get is two speakers producing the sound instead of 1. I'd stick with 8 ohm speaker in series rather than drop to 4 ohm - it looks like it isn't ideally designed for an 8 ohm speaker given the transistors used.

I don't think using a BC337 will make much difference.