I don't have any experience with round bale belts, but I have done quite a bit of conveyor work, I'll try to help.
1. Belts do stretch. Yours may have a take-up system powered when the machine is powered. Power on, take up system takes out the slack. This is a possibility, like I said, I don't know round balers.
2. You do need a special tool to attach the hooks. There is the old style that crimps the hooks on, and there are the roller lacers. Roller lacers are sweet to use and easy.
3. Yes, always attach the hooks to fresh belt. The most important thing here is to use a square. Make absolutely sure your cuts are exactly square or your belt will track off to one side and you will never get it to track straight.
Also, after installing your belt, do not track from the end or drive pulleys. Always track from an idler. If you change the geometry of the end or drive pulleys, it will stretch your belt on one side and throw off the tracking, basically ruining the belt. When you adjust the tracking on your belt, watch the lacing go around 3 times, then make a minor adjustment, watch 3 times again before adjusting. Go very little with your adjustments unless your belt is rubbing on something.
This is just generic belt repair/tracking info. Like I said, I don't know round balers. But I do have some good experience on warehouse conveyor systems. I was maintenance manager of a warehouse with 3.1 miles of conveyor and loved to get my hands dirty on it.