Explain the Apple Watch Sport and series 1 to me?

Does the Apple Watch Sport have the same capabilities as the newer models? Can it play music via Bluetooth? Does it run apps the same way iPhone does? Does it work with music apps like YouTube or do I have to pay for Apple Music? Can I put songs on it like an iPod? IMPORTANT: if I buy a watch sport or series 1 from Newegg or ebay can I purchase Apple care and add it after I've purchased? Or does s it need to be insured as part of me buying it?

The Apple Watch Sport was part of the 1st generation of Apple Watches. Currently only the Series 1 (not to be confused with Gen 1) & Series 3 are available & neither has the Sport model.

It can control music through bluetooth.

There are compliment apps available for the Apple Watch. I wouldn't say any of them run apps like iOS except in the sense that they are available for the watch & allow features of the iOS version to be done on the watchOS version.

I'm not aware of being able to play YouTube music through an Apple Watch but you should be able to control a video's playback on one.

There's the option of a playlist for the Watch, though I don't think it holds songs itself.

I believe AppleCare can be applied after the fact