Tell us about yourself!
The transformer ratings are definitely non-critical. As this circuit uses the flyback topology, the ferrite cores must have a tiny air gap between them.You could use any small ferrite transformer for this. It's the turns ratio that's critical. A good way to estimate it would be to divide the output voltage required by the input voltage. For fast charging I would recommend keeping the turns ratio around 1:10.I'd highly recommend trying to wind your own transformer, it's easier to keep everything under control and definitely rewarding!All the best!
Even I'm going to build a similar prototype soon. The coil should not be wound around the rails but on top of them. Refer to left hand rule and right hand grip rule. I don't think you can put a spin on the projectile this way. It's better to put the coil in series with the rails. My YouTube channel:https://www.youtube.com/channel/UCoqOSu_2aKcgYsi7_...
Yep, you can. Usually carbon or graphite are better than metals since they do not 'stick' to the rails.