If I change platforms from Windows to Apple IOS, will I be able to transfer the tax file that I am working on. I probably have to order a IOS compatible Turbo Tax software, but will I be able to continue on my tax returns that I started in Windows?

Yes, if you are using TurboTax Desktop (CD/Download product), all of the .tax data files are compatible with both Windows and Mac.  In addition, the CD version includes the software for both Windows and Mac.  If you had a download product, you would need the separate Mac version.

If you prepare using TurboTax Online (website product), then your returns are all saved in your account and are accessible on virtually any computer or mobile device that has internet.

There's no critical limits when using the Online Browser-based software  (other than only "one" tax return allowed and no "Forms Mode")
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But be careful on your OS terminology here...
...the downloads work on MAC-OS versions, but not on iOS versions (unless I'm grossly mistaken).  But check here

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