You can’t upload music via the app. The add to library button is used to add music to your personal library with an all access subscription. You have to go to the actual Google music website and download an app that you use to upload music to the cloud.
I use my Nexus 7 to read all my bio and chem textbooks with Adobe and it has been butter smooth since the last Adobe update. Not as feature rich as some PDF readers but much smoother IMHO. Definitely suggest getting it again for you. FYI my textbooks are all roughly 1250 pages as well and I get no stutter except for the very first load of the book.
If you go to the music labs section and disable the HTML 5 option then the chrome book will perform much better. Its a known bug with Chrome OS. Also if you go to www.YouTube.com/html5 and leave the trial then you will also get much better performance. The local video playback sucks though. I set my NAS up as an FTP and that’s the only way I can get it to stream. Some .mkv work well and all .mp4 work perfect that way. If you upload a video to Drive than you can also stream it in a ‘YouTube’ like interface in various resolutions and it works perfectly. The only downside to that is that you have to wait for processing for that to function and it can take an hour to overnight depending upon the size of the video.