1. Without seeing what you want, it is hard to give you advice based on your description. In general though, beam type animations are done with particles, tiled backgrounds, and blending modes.
2. If you want to animate a bow at runtime through code, you can use the drawing canvas plugin to draw the line, and animate it by numbers. This is significantly harder than doing it the traditional way though, which is to simply draw multiple frames for your bowstring animation.
There might be some sort of distort effect that you might be able to utilize, but again probably more effort than its worth compared to just drawing out the frames.