There are some fountains like this in Airports and where the tapwater is pretty bad, but usually a public water fountain is an old fountain from the medieval times with some ornaments and stuff
This is the one from my home city
But they are only outside because on the inside you just fill your bottle in the bathroom
since you don’t have another phone, I think the risk is too high to repair it. It’s the best option for sure (for the planet and for your wallet), but if it breaks you don’t have a phone at all.
That being said, if you want to learn how to repair phones, you can live with loosing the money for the screen and if you can live without a phone for some days in the worst case, I think you should still go for it. It’s a great skill for the future.
Not all, but a lot of them. If you encounter a fountain that looks like you can drink from it and it DOESN’T have a sign telling you it’s non-drinkable, you can safely drink from it