My friend has a iBook G4 with OS 10.3.9.
10.3.9 does not recognize the iPhone, which requires 10.4.10
So he can't sync the iPhone with iTunes.

He wants to be able to put videos onto his iPhone to watch.
The only way I can think of is by syncing and watching with the ipod video section of the iphone.
But he can't sync with iTunes.

So is there an app that he can download (from App Store or Cydia) that can watch videos?
If so, how does he get videos onto the iPhone?
iphonebrowser work with OS 10.3.9?

I would recommend the Air Sharing App from the App Store. It was free but is now around $6 IIRC. This way you can create a bonjour share on the mac and tranfer files easily.

It will display and play all iphone supported media.

Cheers