I'm not a technician but since I noticed that the new Plex player has some problems with the AAC created by ITunes I wanted to do this test. Normally I create my AAC with a program for Windows (http://xrecode.com/) that uses FFmpeg libraries but I have not noticed any gaps with your player
The app does report playback to the Plex server you're playing from, so if you have last.fm support enabled in your plex.tv account settings you should be getting scrobbles.
Having said that, I do plan on adding native last.fm support in the future so it works for those using iTunes/Apple Music libraries too.
Glad you like the app! Feel free to ask questions / share any feedback you have here.
It's possible I broke something with 1.1. It shouldn't show as "Offline" unless plex.tv reports it as being unavailable.
Can you disable wifi then send me a report through Settings -> Report an Issue and I'll take a look at the logs
There might be a way but I don't know how you would sorry.
I did a little digging and it looks like importing playlists into plex is difficult. You can export to a m3u8 like this webtools next gen. It was easier on original webtools but I think that has been discontinued. Then this website can import to plex, but I think it is very limited in terms of free options and requires a subscription. Probably not worth it.