When installing ESC on the frame, should I remove heatshrink from the ESC's or leave it on?

Shrink-wrap covering is important to isolate components from carbon which is ground.

Always use heatshrink for your ESC if installing on the arms.

True in general, but heatshrink per se is not necessary. Always insulate any electronics from carbon, but heatshrink is not necessary. You may use a foam pad, you may conformal-coat the whole ESC or do something similar. Removing heatshrink may improve thermal profile of your ESCs.

I typically remove the heat shrink and mount the ESC on 3M 2-sided sticky tape, then a couple wraps of electrical tape to hold it in place. Just don't use zip-ties, they can damage the components