Ubuntu – Emulator for iphone/ipod/ipad apps

While some older versions of iTunes can currently be made to work with Wine (or Crossover), they cannot be used to update or sync newer iPods

The reason is that Wine lacks a handler for Windows USB device drivers, and the iPod acts as a custom USB device. This is the same reason that software that requires a special key dongle also doesn't (yet) work in Wine. There are some preliminary patches available for this, and you can read more history on the Wine wiki, however don't expect anything to work.

The only iPods that currently work in Wine are really old iPods that act as simple USB mass storage devices. And even then you still need to find an older, working iTunes.

Because of this problem in Wine, to do the firmware upgrade you'll need to either setup a virtual machine with Virtualbox or VMware or, perhaps more simply, borrow someone else's computer.

You can run the apps from Android with an Android emulator, see this was asked before: Can I run Android apps on Ubuntu?.
Maybe you can re-compile the source of some app to work on linux.
Would you explain better the similarities you found between deb and apk?
Finally, about the quality of apps, I think it is a matter of opinion. In my opinion, linux has the greatest softwares available (thanks to the community cooperation and efforts).