1. Yes, you can track distance. Apple recommends an initial calibration of 20 minutes of walking or running in a flat area (doesn't have to be 20 minutes all at once) while the watch is connected to the phone (see: https://support.apple.com/en-us/HT204516). It's not a requirement, but it supposedly helps with accuracy on subsequent runs and treadmill runs without the phone. If you're not using the native workout app for runs, then this might be irrelevant.
2. From the native "Workout" app you can display up to 3 metrics on the screen at once (calories, distance, pace, heart rate). I haven't used Mapmyrun or other apps on the watch or any other running apps so I'm not sure there.
3. Yes, you can sync selected playlists from iTunes to the watch and play them without the phone and use bluetooth headphones. I believe you get either 1 or 2GB of space allocated for music.
4. Pausing and changing music from the watch, while possible, is a bit annoying during a run. There's a music "glance" where you can swipe up and use music controls, but glances only work from the watch face. This means you have to leave your workout app, go back to the watch face, swipe up, then change/pause/play your music. Very distracting and annoying on a run. For now, just so I could compare metrics with my go-to apps on my phone, I've been running with my phone AND watch, so it's easier for me to just change music from the lock screen on my armband.
Overall though, I've been pretty happy with it. I haven't had any other wearable fitness devices before and it's nice to be able to glance down quickly to view my stats and progress as well as get extra info I haven't had before like heart rate. I do hope they remedy the music control annoyance, but I can live with that for now.
I don't have my watch yet, but have you tried Siri for music control? Siri can control the music player on the phone, but since the controls are right there one wouldn't normally use it. But it will pause and skip to next song. That seems about all that one would want once you've started your running mix. Can you try it on your watch and see if that works and let us know?