Can't figure out how to sync my iPad Air properly

Hi everybody,

this may be a bit OT but I figured, since Developers hang out here they would know what to do ;-)

My new iPad Air was delivered today, i backed up my "old" 3rd Gen and made a full restore and sync with the new one.

For some reason though, not every app and not every book was installed on the iPad Air nor do any of the missing ones show up on iTunes (Software)

This might be connected to me having two accounts on iTunes in two different Stores.

But even this does not sum up.
For instance, I have bought Asphalt 7 and 8 with the SAME account. However, only Asphalt 8 shows up, not 7!
Both instances are still installed on my 3rd Gen with the same account associated.

Also I had ~200 books on my 3rd Gen, but only 127 got transfered to the Air?
In this case, almost all books, be they PDF or EPUB were "uploaded" to iPad via Dropbox and from there "opened" in iBooks.

I *think* I may have solved the book thing by manually deleting ALL books from the iTunes Folder on the PC and then again put all books into the "Add to iTunes" Folder. This seems to have done the trick, at least the new numbers add up and the bookmarks seem still intact.

But for some reason, I can't seem to access the "missing" apps?
All of them are still installed on my 3rd Gen, but show up neither in the iTunes Software nor on the Air, whichever account I log in.

Sure I could install them all manually, but I fear that I will lose progress in games and content in apps?

Any suggestions?

Edit: Just to mention it: None of my devices has ever been jailbroken or has been tampered within in any other way. All totally legit ...

 

Some software from a Chinese site?
Ida now?

Meanwhile - through trial and error - I have somehow managed to get the "missing" Apps from mit 3rd Gen into the iTunes Software.

Then I connected the Air and it looks like they are now all copied to it. Only takes some time and is at 50% now ..

However, it can't be that it has to be this complicated, can it?