You are correct on all three counts.
The Workout app will work without your iPhone, at least. Third-party apps might need to be updated to be completely independent. Strava, for instance, won't start without an active iPhone connection, but Runkeeper will.
Both the first generation WATCH and Series 2 support syncing of a single playlist up to either 2GB or 250 songs.
I thought it was time to share my experiences with using sleep tracking apps on my Apple Watch.
Not long after posting the question I downloaded Sleep++ and used that for quite a while. Sleep++ works well. It is power efficient and met most of my requirements. It's not perfect (e.g. you need to manually start/stop sleep tracking, but it's free (with ads - but the ads don't appear on the Watch) so you can give it a good try before paying to remove ads. It's also very well supported by the developer.
My hope was to use this app until Apple's own implementation of a sleep tracking app in watchOS was released. But since this wasn't ready in time for watchOS 4, and since I upgraded to a new Series 3 Apple Watch, I decided it was time to look at another sleep tracking app - namely one that doesn't require me to manually start and stop it (for those times I forgot, or those times I dozed off unintentionally).
I settled on AutoSleep which is a paid app. I've been using it for a couple of weeks and have been very impressed with how well it works and how it meets all my requirements.
It can automatically detect your sleep (assuming you're wearing the watch) or you can use it manually (similar to Sleep++ but without having to wear the watch). Obviously using it manually is not going to provide all the measurements, but it's equivalent to what Sleep++ could do.
Also, if you're wearing the watch, you can manually enable the Lights Off option. This is not necessary, and since one of the best selling points of this app is that it automatically detects your sleep without manual intervention, you may not want to opt for this. But if you do, it tells the app that you've officially gone to bed (hence the 'lights off' label) and the app will also track how long it takes you to fall asleep after going to bed. Useful if you want to also track that metric.
One of the other great features of the app is that on the iPhone you can tweak it to suit your sleep. That is, the app provides some nice measurements and graphs to illustrate your sleep and, if you notice it hasn't detected your sleep accurately enough (e.g. you know you woke up during the night and the app hasn't detected that), you can alter how sensitive it is or isn't to tracking your sleep. For me, I've never had to tweak it. It has accurately recognised my start sleep time, as well as my restlessness and any time awake in bed during the night. It has also detected times that I've dozed off in front of Netflix, while reading a book, etc regardless of the time of day!
All in all I am very happy with this app and it's very close to how I imagine Apple will implement its own version.
As there is no free version available, feel free to ask me any questions about this app in the comments below.
NOTE: I am not affiliated with this app in any way.
Best Answer
Yes. The Apple Watch Series 2 doesn't need to be paired to an iPhone to utilize GPS tracking because it's built in.
From a MacWorld article on the AWS2 and the GPS functionality:
And from Runners World on the GPS functionality and the accuracy: