You will find that in some seasons and heavier use your pool will require water more often. You can have a automatic water level maintainance put in but during cooler monthes you'll add none. If the water gets below the intake you can burn up your pump. watch you level.
You should add shock to your pool when the water needs a boost in sanitizing power, typically after heavy use or if the water appears cloudy or has a strong chlorine smell.
The water should contain chlorine in order to kill germs. You won't know who or what might land in your pool.
Add salt
Remove some water in container (10-20%) and add new water. example: pump water high in cyanuric acid out of a swimming pool and the add fresh water to the pool.
If it's cured sufficiently to add water, it should be cured enough to use.
Yes, you should run the pump when you add chemicals to your water,
I should add, no chlorine in water.
Normally, about once per week. Possibly, up to 2" to 3". K
You need to replace the water that evaporates.
Reduces alkalinity of swimming pool water (softens hard water)
Yes
You should add a few granules to some water, and then add this water to your hot tub water a very small amount at a time. See the related link I posted for more information on testing and using the chemicals.