Can't listen to music on iPhone, can't sync iTunes and iPhone any more

Hi, I have a few problems ever since new iTunes came out:

1. All of a sudden I can't listen to the songs that I saved as My Music but didn't download the actual files on my iPhone 5s. This used to work until now. Now it doesn't
2. Can't sync music from comp to iPhone. Here is the detail description:
   1. I connect the iphone via cable to my MacBook Pro and turn iTunes on. ITunes recognizes my iPhone and all is well
   2. In iTunes, I click on the iPhone icon, scroll down to Music (where I usually check the songs to sync). There I have a message "iPhone can access your iCloud Music Library..." and it's not letting me see or select songs. Since this is on, I though the problem number 1. would not be happening. But I can't listen to the music not downloaded to my phone when I'm on the street...
   3. Then I go into iTunes 'Preferences", uncheck the iCloud Library and turn off all the sharing stuff so I can pick and chose my music to download to my iPhone so I can have it at ALL TIMES!
   4. After "unchecking", i unplug the iPhone, and plug it back in (to make sure changes propagated, I guess). Well, no changes have taken place on iPhone/Music tab - still the same message: "iPhone can access your iCloud Music Library..." and I can't select songs.
   5. I then exit out completely from iTunes, start them all over again, plug in my iPhone again, and the same thing happens - I can't check the songs to download to my phone.
3. The last problem that I have is that, when listening to iTunes on my iPhone, every time a newtork change occurs (either I leave my WiFi and switch to cellular, or when there is no network), the playlist (playback) STOPS, as if somebody clicked pause button on the device. That never used to happen before. Network change never had any influence on my music, except of course when listening to radio or listening to a song not downloaded to the phone.

To summarize: bottom line is I want to be able to listen to all of my music on my iPhone like I used to be able to. Preferably without interruptions caused by network changes.

Please help. Thanks

P.S. iOS 8.4.1, and OS X are the latest version - I update immediately.