I think 5 is perhaps a latency issue, and because there's no feedback when things are happening it seems non-responsive For instance, if it's buffering a song ready for playing, a progress bar or even a spinning circle would be nice, rather than me clicking Play a few times because I'm not sure what's happening. Likewise, when I click a song to open up the "Play or Download" right menu, nothing tends to happen a lot of the time, and I'm not sure if it has ignored my clicks, or whether it's just doing it's thing and catching up (I suspect the latter). Ideally, if you can open up the right menu (the Play or Download one) as soon as I click a song, even if you then have to do loading stuff before play works it would seem more responsive. Just remember the user needs feedback to know something is happening.
Regarding download button, perhaps "grey it out" for now, and put a "coming soon" near it or something?
Anyway, these are nitpicks that are easily fixed, I think the app itself is a pretty awesome effort.