How to back-up specific apps and information from iTunes?

I had a 64g iphone 6 that had a hardware problem and could not turn on because it froze mid-way in the restoration process. As a result, I turned it in to upgrade to a 6s with a program my phone company has. Being in the financial difficulty IIm currently in all I could afford was the 16g iphone 6s. I know I can't back up everything but there are some apps like my password protector app and a bunch of important, sentimental notes from my old 64g phone that I need.
It has to be through iTunes because I only backed it up through iTunes. I stopped using iCloud because of that glitch in the upgrade where you had to pay for storage a while back.

How long does it take Apple to process and iPhone order?

I just ordered an iPhone 6 yesterday and it's supposed to be delivered tomorrow. But on Apples website it still says processing. Is it going to make it on time? Did Apple just forget to update the status?

Added (1). *An iPhone order. Not and. Lol*