When you go to the grocery store, and they have one of those machines that fill your five gallon jugs with pure water, go look in back!
The water comes from a tap in the wall hooked up to the local municipal water supply. But it’s better and purer than the same tap water at your house.
You Betcha.
For sure.
Depends on what's going on inside the machine. if there's a membrane filter (essentially what Brita filters use) or a reverse-osmosis filter (what the bigger, pricer systems use and what most industrial bottlers use), then you're getting water basically identical to what you are buying in the bottle and what you can get with a filter at home.
I occasionally buy bottled water, when I'm out and about and -- here's the thing -- I want it ice-cold. If you can find a water fountain, it's likely to be a little cooler than room temperature, but not much.
When I take the time to plan ahead, I refill bottles from the filter at home, putting some in the 'fridge and some in the freezer. Take a tiny cooler -- something like one of those insulated lunch bags -- in the car with two chilled and two frozen bottles, and by the time you polish off the cold ones, the frozen ones will be partially melted.
I use the same trick at the ball park, but I have to buy water for that, because they only let you bring in factory-sealed bottles of water, to keep folks from smuggling in vodka. A couple bottles cold, a couple frozen, and the frozen ones are ready to drink in about the 5th inning.
For me, the filters are purely for aesthetics -- my local water supply is excellent, and I have no worries about its safety. There's a little chlorine taste I don't especially care for.