Q: What happens to the videos in my photo stream?  They do not get sync'd to my computer?

Videos are only added to shared streams.  If you added them to a shared stream and invited yourself as a subscriber, and your computer meets the system requirements for iCloud photo sharing (see http://support.apple.com/kb/HT4083), then they would appear on your computer.  Otherwise you would have to import them to your computer as explained here: http://support.apple.com/kb/ht4759.