If you view videos online, are the videos stored somewhere on your computer?

Usually everything you're browsing on the network is stored in the browser's cache. Depending on the site restrictions, movies, flash files, java applets, images, sounds and so on are stored locally in the browser's cache folder.

Well if you see video online such as maybe youtube or google and like the video want to download it. Takes a couple of steps for this process so that you can see first have to go to a site where they want you copy the url of the video. Then once this happens it will be downloaded to your desktop. The Video you will find one these website have a format of Flash.flv and since many people don't have flashplayer on their computer you will have to get a converter that can change your flash movie file to a mpeg or avi which then you can view on the computer.

Most of the online video websites only PLAY the videos. It isnt stored on your PC in any way. However there are some soft ware / plugins that allow you to record these videos.

No, they aren't, they are stored somewhere else but not in your PC