LOL, I go back and forth all the time, and so does my horse. Mostly you'll want to just start asking for a lot less collection, more long and low work on the flat, but always forward. Low gymnastics to get him started over fences, and try to ride him as close to the base of the fence as possible to teach him to rock back and keep his front end sharp.
Shorter stirrups, more lower leg, less seat, and the nose slightly in front of vertical. You always want him to take long, smooth, sweeping strides. Think something between a working and and extended gait.
Sure!! My guy is a solid adult amateur and amateur owner hunter, and is also currently doing 2nd level dressage.
There really isnt much difference, if you have a horse that is suitable for both.
For hunter, you still will want him to take a contact, but just "modify" it slightly so you dont have him ever past verticle. Often a nosepoke is warranted too. I wouldnt worry about this so much for jumping, as they generally do come ahead of the verticle when jumping around a hunter course.
When jumping, rhythm needs to be the same, no change. Your dressage training will help you get lovely corners that a lot of hunters skimp out on.
Base the pace on his stride length. The monster strided horses will need a quieter pace, but if he has a 12 foot stride, then you will need to "move along".
Practice lots of canter, there is almost zero of anything else done. If you have a good rhythmic canter, with no pace change, with no bobbles and no choppyness than you will do just fine. The jumps come from the canter.
If he's doing 2nd/3rd level, you'll have a great head start in the hunters! After all, the jumps are only 8 of the strides of the course, the rest is flatwork. Your horse should be very adjustable, soft, and flexible, which will all benefit you in the hunter ring. I second gymnastics to work on the basics of jumping; once he learns how to rock back, the fence heights can start to go up.