Welcome to the fun world of old trucks! You mentioned the door handle falling off- look foe a little hole on the inside of the handle-- it should have a little set screw that is turned either by an allen wrench or, if the top is slotted, with a screw driver. If you push on the handle and tighten the screw it may solve your problem.
The carb may be leaking because the float is sticking or misadjusted rather than needing a rebuild.
Beautiful truck-- good luck with it.
Glenn