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do try the process again and make sure you dont wipe until all has been transferred to your android device . you also have the option to download pc companion and transfer all on iphone via pc companion
I'm almost sure the Xperia transfer has Two versions - One is not compatible at all as it is for Android devices only and the other will not transfer apps
So this one won't work at all https://play.google.com/store/apps/details?id=com.sonymobile.xperiatransfer
and this one will not transfer apps https://play.google.com/store/apps/details?id=com.sonymobile.xperiatransfermobile
PC compainion will only see your iTunes backups and restore from that.
I had all my contacts on my macbook, opened the contacts app, selected all then emailed them as .vcards to my gmail account, opened them on my Z2 and it imported them all nice n' easy.
Sounds like your best bet might be to sync your calendar & notes with a gmail account then bring them in to the Z2
hope that helps 