Why are Photo Stream process running, but photos only loads when iPhoto is opened? I have a process called Photo Stream running, but I have been discovering that my photos in my photo stream only loads when iPhoto is opened.

Why?
This is primarily targeted towards Shared Photostreams. When someone streams a picture you will get notified (via Notification Center) that a new picture/comment (or like on your photo) has been posted. As a result this process must run all the time.

iPhoto only loads/displays the photos for you to see.

If you desire to disable it, you can go to open System Preferences -> iCloud -> Disable Photo Stream.