Can't transfer purchases from device

Hi,

I'm using an iPhone 5c. I have the same problem as many others, which is that Mail doesn't free up memory even after deleting all email accounts from the device. Settings now shows me 0 bytes as available on my phone, with Mail using up over 1GB of my 5,3GB capacity despite being completely empty.

I know the only way to get around this bug it to back-up your iPhone, restore it to factory settings, and then restore it to the back-up, but I'm having problems with creating said back-up.

I have some paid apps on my phone that aren't synched to my Mac yet. When I go to transfer purchases from device, it tells me it cannot be "synced" because of not enough available space - I don't want to sync anything to it, I want to transfer the apps to my iTunes in order to then create a back-up.

Help please, this thing is virtually unusable, thanks.