If you boot from the backup and represents what you want, you can restore that in full. You can't really just restore "Mail", because it has parts all over the place.
With regard to the non-SD stuff, Apple isn't making you use WiFi. There's a version of iTunes available that lets you install applications using iTunes. But I do generally suggest solving your WiFi problem so you can move forward eventually... it's a lot worse to have hackers "nosing into your life" because you've fallen well behind the security patches then to worry about Apple doing so when, generally, they're really not: they're very privacy-first in their approaches.
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--Dave Nanian
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