Is there any chance to attach and use the Nitrokey Pro with an iPhone?
And which software should I use to decrypt/encrypt my emails and files?
No, you can’t use a Nitrokey with iPhone.
What is the reason for the missing iOS support? Hardware, Driver, Licenses, NDAs, not yet tested…?
Please understand this question as “feature request” of a satisfied customer 
I think many customers are interested in a “one size fits all” solution for all their computers and mobile devices.
Edit 09/25/2016: Even the YubiKey from yubico (a major competitor to the Nitrokey) does not really support the iPhone/iOS
due to “changes in the Apple firmware over which we have no control”:
yubico.com/faq/yubikey-ios-device-ipad-iphone/.