As for fighting, you have to train. A lot. You need to train yourself to relax when you're punching - the tenser (yes I know that's not a word) you are the slower you punch. But it takes a lot of work to get to the point where you can throw quick punches. Speedbags can help, to a point, but you have to be careful with them. You can easilly get in the habit of throwing quick fluttery punches that make the bag move nice and pretty but wouldn't do any damage in a real fight. You don't wanna train yourself into that corner.
Now, here's a trick to be quicker than you really are. You probably fight like most people - that is you put your fists up, and hold them there until you throw the punch.
Try moving your hands around. If you watch good fighters, their hands are always moving. The eye is VERY good at quickly seeing something go from motionless to being in motion, and the brain computes the trajectory of the new motion very quickly. But they're not quite as good at seeing motion flowing into a different motion. You'll gain a speed advantage if you keep the fists moving.
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