Hi Mary. I found several articles on this. You can just google it if you want to. But synthetic potassium is potassium this is "created" to simulate real potassium. Sort of like beauty products that have synthetic Vitamin E in them. They can mimic the real thing, but they don't work as well and are not good for you. The potassium in bananas and things such as coconut water are naturally found in those foods and they are in their pure form. Your body really can't assimulate synthetic foods. But the body can absorb and utilize foods that are natural. Gatorade is full of synthetic stuff and sweetners.
This is not true. The importance of potassium is as a blood electrolyte, where it exists as an atomic ion K+. There is no such thing as artificial potassium. Sports drinks supply your body directly with K+ ions (through some kind of dissolved salt) and your body absorbs them very readily. Bound potassium in natural foods will in fact be a whole lot harder to absorb and it'll take somewhat longer for them to enter your bloodstream. That's fine if it's what you want, but if you're severely dehydrated, it's definitely not what you want.
For rehydration you want something that is isotonic, which means that it contains electrolytes at or close the same concentration as your blood, which is essentially optimal for rehydration, since your body has to maintain its blood electrolyte concentration regardless of its water content. This is why giving people suffering from severe dehydration pure water is a bad idea: if their electrolytes are low, then the blood concentration becomes even lower due to introducing water and the body will immediately produce urine to get rid of the excess water and maintain the concentration. Producing urine in itself leeches further electrolytes from the blood and they actually end up even more dehydrated than before. Rehydration fluids should always be isotonic.
Some sports drinks contain electrolytes, but I doubt they're truly isotonic, since proper isotonic rehydration drinks taste pretty nasty. The artificial sweeteners are a separate issue. They are basically there to hide the nasty flavor of the electrolyte salts, since the drinks would be pretty unpalatable otherwise. Sports drinks are probably better than water for general hydration, but probably shouldn't be used for people who are truly dehydrated unless they really are isotonic.
In normal conditions, it's fine to remain hydrated through natural foods and pure water, since you basically dump an excess of everything into your body, and it'll then just get rid of the stuff it doesn't want. If somebody is suffering from dehydration, on the other hand, the artificial stuff will give them a significantly greater chance of survival.