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most video streaming sites will not work with Safari, due to the lack of flash because it's too cpu demanding and resource hogging. Some sites will have iPhone/Mobile versions though.

The iPhone cannot record video out of the box. You need to jailbreak it and install Cycorder via Cydia or Installer.
 
1] To record Video's you'll need to Jailbreak your iPhone.
Google it if needed. Cycorder is an amazing video recorder.

2] I think only the MPEG-4 Video's can be played through Safari
 
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