here are my thoughts on the 4 questions.
1. if this population explosion is as big as you think, thier movements will probably not alter all that much at this point. maybe back in the pup rearing months because the parents (fox & coyote) didn't have to travel as far away from the den to catch a meal and bring it back. but now that the pups/kits are out exploring and for the most part all but self sufficiant. i'd say they are out stretching thier legs and checkin out their parents turf quite well.
2. no, the pups/kits should disperse as normal. the parents don't kick the kids out not only because of food management...but because of genetics. just because there is a bounty on bunnies mom & dad will still bump the kids out(mostly males).
3. if this surge in bunnies in your area has been occuring for some time before you noticed...you may already have larger litters in your area. its a fact of life for most all animals...if the food is plentiful..have more kids. its a natural cycle to expand the population. if this is a recent thing, just this spring & summer...you may have more next year. but the 'boom' will only last so long mind you. if a prey species is in large abundance it is because of natural factors such as you stated..weather. also because there may seem to be a lack of predators in your area to allow such a 'boom' to occur....fox, coyotes, hawks, owls..etc. like i said, this 'boom' will only last for so long because all the predator species will bump up thier number of young because of the abundance of food. this climb in numbers will only last to the point where they extinguish their supplies. if they eat themselves out of food....the cycle reverses...the bunnies #'s go down and the predators are soon to follow. its called a numerical response and there are many, many studies made over the years of different predator and prey relationships as far as populations.
i could ramble on and on...but you get the point. if you want more examples or reading material on this let me know. my text books are doing nothing but taking up space on the book shelf and collecting dust.
4. call response may actually be affected, but not by much. calling is more to trigger curiousity than filling an empty stomach. fox and coyotes both will respond if thier bellies are full....or have food in thier mouth. but probably not with the enthusiasim as if they were really hungry mind you. i've seen video of fox & coyote both lounging in the shade digesting while the hunter was blowing his brains out on a call...and they just sat there. i've also seen fox & coyote respond to a call with somthing in its mouth. ask Slyfox about the coyote he and his brother called in last N.C. hunt...it had a grouse in its mouth when it showed up.
one thing is for certain about mother nature.....nothing is for certain. nature has entirely too many variables to be relied upon 100%. just when you think you have a critter or habitat figured out...it'll throw you a curve ball. nature is very complex.