Am I doing something wrong?

Is the built-in Photo app on the iPhone/iPad/iTouch as stupid as it seems, or am I doing something wrong?

All I'm trying to do is manage the photos on my device in the most primitive way. I'm not trying to retouch them, share them, or photoshop them. All I want to do is manage albums or folders, including photos taken with the iPhone and photos downloaded from my computer. Here's all I'm trying to do:

1) Rotate pictures that were taken with a camera held in a sideways position (pictures downloaded from my computer, not taken on the iPhone).
2) Reorder the pictures in an "album"
3) Delete pictures (other than the ones I took with the iPhone).
4) Create new folders or albums and move or copy pictures from one to another.


All the pictures I take with the iPhone camera go into a default album called Camera Roll. I can delete these, but cannot reorder them or move them into a different album.
Pictures downloaded from my computer are totally unmanageable. They cannot be deleted, moved, reordered or even rotated!

Am I missing something here? My last two phones, which weren't even considered smart phones, offered the ability to do all of the things I listed above.

If this is really all there is in the iPhone Photo app - is there an app that I can download that will let me do these things?