As far as I can work out, from incomplete downloads, ticks denote all downloaded ok.
The manually manage option is for those who want to tailor their library collections in Music and Video to specific items. If you have this ticked, then it will sync with the sync selections in your devices pages (eg, Music, videos).
If you want to sync all of your collection 'all' the time, leave manually manage off and put the a tick in the devices' page to sync all items Dependent on iCloud use, and or automatic download options in iTunes, new purchased items are added and synced automatically as they are added - this only applies to Store purchased items.
If you are going to added content outside of the Store, then Manually Manage is the option to take for Music and Videos - it does not affect anything else. IE Apps or podcasts, etc.
If you have manually manage off, and 'selected playlist' option ticked, then it will sync existing ticked items, but new items downloaded will require you tick them (a) after the next iTunes automatic download when it connects to the store and downloads any items, or (b) you download to a device and then sync the device, in which case it transfers the new download to your library - but, as happened to you, deletes it from your idevice.
Retcicking and resyncing will add the item back on next sync.
Don't forget that whenever making any kind of manual change to hit Apply and resync, to stop changes being lost.
However, and i cannot stress this enough, iTunes is very problematic, especially when handling large collections. Its sync operations can be erratic or non-functional at times (even buggy perhaps)
If all options fail, then go to your program installation control folder (Control panel\Programs etc on windows) and select to repair iTunes.
And if you have not already got it
http://help.apple.com/ipad/5/interface/ the ipad manual (not the used guide - this is more about how it operates)
may prove usefiul to you.
Best wishes, Ct
