Re: increasing handspeed
Basically, it's a coordinative issue. Get better at punching (from punching heavy bags, mitts, sparring) and you will get better at utilizing the speed of your muscle contractions, however fast that may be. This is why generally fast guys can feel sluggish and slow when they first start boxing.
You improve your speed from then on by doing speed-strength training. Such as plyometrics, certain weightlifting movements, etc. Short, all-out intervals on the heavy bag (type sprints) works well.