Buying an apple watch

Not at all, thats the nice thing about it. Perhaps surprisingly, even something like paying with Apple Pay works on the watch alone. This is true for the GPS only model as well.

Tracking outdoor workouts like running are generally fine too. Check here for details for instance:

https://www.techradar.com/news/wearables/can-the-apple-watch-work-without-an-iphone-1288140

What are you planning on using it for? If it is to conduct a workout and record everything you do not need to have cellular, it will transfer the data the next time you are within Bluetooth range of your iPhone. If your gym has WiFi and the watch connects you will be able to get iMessages, etc. If your carrier supports WiFi calling you should also be able to do that.

You will only be able to use Pandora if your gym has WiFi and your Watch is connected to it.

Yes if it's the cellular version of the watch,otherwise your phone has to be in bluetooth range if it's the GPS only version.

Yes it does.