I got my iPhone replaced yesterday. I didn't have a recent backup on iCloud so the genius told me that I could just back it up to my MacBook Pro, even though it is not synced to my MacBook Pro. I did and I came home to restore it. Restoring it from the Backup on the MacBook Pro doesn't restore the apps and the app layout like he promised me it would. Was he wrong? Can a backup to a non-syncing computer restore everything back to the phone, including apps?
No, even if you haven't synced your phone for a while your media should still be in your iTunes library. All you have to do is sync with iTunes to transfer it back to your phone. If you had purchased apps or music on your old phone but didn't sync to transfer these purchases to iTunes, all you have to do is re-download in iTunes for free and sync them to your phone. This article explains how to download past purchases: see "To download previously purchased apps, books, music, movies, or TV shows to your computer" here - http://support.apple.com/kb/HT2519.