Hi,
I have developed software for over 20 years, and iOS apps for over 3 years. You can see some of the apps I wrote by searching for "naxomedia" on the App Store. While very different from your project, they illustrate the use of many iOS technologies, include fetching images, sync with a remote database, push notifications, in-app purchases, ads, analytics, galleries, social sharing, etc.
I will provide a native iOS app, compatible with iOS 7 and iOS 8, with the requested functionality, except the "editing" (point 14) and login (point 15), which would add an extra 500 euros.
Also note that I don't think your choice of gesture is the most natural. I would recommend using pinch/zoom to change the number of tiles displayed for instance.
The milestone needs to be funded prior to the work beginning, but you can release it only once I have delivered the app.
Note that the time given does not include validation time by Apple (which takes about a week, more if they have any issues). Also, you will need your own Apple iOS Developer Program subscription to submit the App. As there is sometimes a bit of paperwork for this, I recommend you start the process for this early to avoid any delays.
Let me know if you agree to these terms or have any additional questions.
Also note that I am based in London, which should make communication easier, as we would be in nearly the same timezone.
Jacques.