1. Everyone's source water is different in complexion and balance. I wont answer what you should do as my tap/well water may not be similar. Ill just say that my water is fairly clean and clear and I dont shock but rather move to the pH/alkalinity first when dealing with a fresh fill.
2. If both pH and alkalinity are low, I prefer to raise the alkalinity, let it stabilize, and retest pH. In most instances I find that the pH levels will rise, as both products are so similar (Sodium Carobonate, Sodium Hydrogen Carbonate).
3. It depends on how much of the product has to be added, how many gallons, etc. If you really want to be strict some manufacturers recommend a few hours between adjusting pH and alkalinity. I dont have much adjusting to do so I only wait 30mins to an hour.
4. For ease, I prefer the water to have circulated and then turned off and calm so that its easier for me to gently dip the strip and get a more accurate read vs having the possibility of one pad bleeding onto the other.
I am sure there are other experts here who have differing opinions. This is merely how I conduct water chemistry but I am always interested in seeing if there is a better way.
I hope this helps. Good luck moving forward.