The bits where blows are alleged to have been thrown or exchanged is irrelevant to the cycling/driving. They are assaults, attempted assaults public order offences or threatening behaviour.
Throwing a bike at a car windscreen????!!! Far out! Did it go through or bounce off? Must have been a chav on a BSO as I can't see any proper cyclist launching their pride and joy at any vehicle. Only way this would happen is if the car driver ran them down throwing the bike up into the air.
Also there is likely much more to this story than has been reported. It may be that the cyclist cutting in front of the car was not the commencement of the altercation. It may transpire that the car driver drove carelessly or dangerously around the cyclist, who took exception, the car driver then harassed the cyclist with his car driving very close to him, precipitating the cyclist to ride in front of the car. Why else would a cyclist ride or cut in front of a car? There is only one side of the story at the moment albeit due to the fact that the cyclist is unlikely to come forward if they have thrown a few punches, whether in self defence or to cause injury, and their bike at the car windscreen. The plot thickens.