I only have a heavy bag, jump rope, different weight gloves, a pull up bar, and some free weights. How could I use these with other body weight exersises to increase my hand speed?

Okay so my suggestion is take your heaviest gloves and start punching you bag but instead of trying to punch the bag as hard as you can focus on hitting the bag as fast as possible have you ever heard of the saying "don't punch at it, punch through it"? Well instead of that think to yourself "punch at it so quick the other person won't see it coming" and use your whole body to thrust your arm forward instead of just throwing arm punches. Also you can do fast twitch muscle workouts such as clap push-ups hope this helped

Double up on your mitt work with your trainer. Mitt punching develops speed and explosiveness. It's no guarantee though of instant speed because handspeed, like punching power, is genetic.

Maybe try learning how to play the drums or juggle some balls perhaps that will help build the speed you want

punch with weights slowly gives more control and more power

Here, try this idea I came up with, its killer -