Yes, you can automatically find youtube videos on itouch, you only have to have the wi-fi from the location you are so that there is a wireless connection. In the menu list it comes already an icon written youtube.
the youtube app and multiple others....it's an iPod Touch not an iTouch
probably the internet connection your using blocks you from using youtube.
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Youtube
Youtube
Youtube...
Yes , there are a lot of websites that has videos school related :) example of that is youtube :)
Yes, it can play almost all videos on youtube except for a few that aren't mobile friendly.
No, YouTube on iTouch does not cost money. There is an 'app' that is already on the iTouch that allows you to access YouTube easily, but if that is not working, just go onto 'Safari' and type in youtube.com and that will take you there cost-free. I hope this helped to answer your question.
There are countless websites that link to youtube videos, it's quite common. Take a look at metafilter.com
There are various websites that will allow one to download YouTube videos and music. These websites, such as KeepVid, will let one paste the YouTube URL of a video into a bar and download it for you.