@Download Complete 3/The most efficient angle will be 45 degrees but anything between 30 and 45 degrees should work well.
This will depend on the height of the launcher and how far back they're firing from. Since the question is about range and the puncher won't be at the target level, 45 degrees won't be the ideal angle. We're talking about the range to the flags without specifying shooting from the expansion zone, the targets are probably higher than the puncher. Then you'll get more range above 45 degrees. Of course, you want to hit the flags as horizontally as possible when the ball arrives, too, so just going for maximum range this way isn't necessarily what you want.
@Download Complete 4/The point at which the puncher hits the ball is probably the most important part. The puncher should hit the ball about 0.5” before it stops. This might take some tuning though. You can significantly increase your power if you get it right.
Yup. I'm glad to see someone suggesting this now. I'll note a nice way to tune is with a video camera. You look for when the puncher loses contact with the ball. You want to see how far it had to go after initial contact, and you want it to actually stop.
@Download Complete 5/ The weight of the puncher arm should be about the same weight as the ball. If it is lighter you will not get the maximum power out of your puncher and if it is heavier you will be putting more stress on your robot when you fire. Personally I would say a bit too heavy is fine.
You're personal preference is actually more correct here. Good instinct/feeling. While the ideal may be the same weight, the collision won't be truly elastic. The question is just how close to elastic it is. With a little bit of loss, the ideal weight of the puncher is close to but a little heavier than the weight of the ball. Again, video can help a lot. You want the ball to fully stop the puncher.
@Anomaly not worry too much about the weight or pullback distance. A heavier puncher reaches a lower maximum speed but slows down less when it contacts the ball, so the weight shouldn't matter much within a reasonable range.
While it's true that slowing the puncher down due to weight won't really matter because the same energy is being put into the puncher from the draw against the rubber bands, one should really worry about the puncher weight. The problem with the puncher not slowing down enough when it hits the ball is that you can end up with a big fraction of the energy left in the puncher after the collision instead of being transferred to the ball. Sure, "within a reasonable range," qualifies things. But that's a pretty small range. The puncher should be a little heavier but not a lot heavier than the ball. If it's noticeably heavier than the ball, you'll have to start adding a lot of rubber bands to make up for the energy you're wasting; the motor and battery will have to do more than really necessary, and you'll put more strain than required on your stopping mechanism.