I have it on both my iPad and iPod Touch. I wanted to download it on my iPhone and I cannot seem to find it. Did they remove it?
Probably. You may still find it under App Store > Downloads > Purchased. You can also try syncing your devices with iTunes on OS X or Windows and then sync the app to your iPhone.
iPhoto for iOS was removed some time ago.
Edit: it was seemingly discontinued when iOS 8 launched.
Why did they discontinue it?
Your guess is a good as mine.
Personally I did use the app from time to time but would hardly call it intuitive or a pleasure to use.
Apple removed it with the IOS 8 update and in the process stole tens of millions of dollars from people who paid for the app. They replaced it with a vastly inferior product, which has far less functionality and usefulness.
That database is in fact a folder. You just cannot access it through normal ways in finder, but not file explorer.I've given up on Apple being even remotely capable of managing user photos in a way that makes any logical sense. I absolutely hate how I have to use an app to access my photos on my Mac because iPhoto and photos create a pointless database file of my photos rather than organizing them in folders intelligently like iTunes.