Well, one of the best ways to avoid going against any copyright issues with pictures, is by using Copyright Free images, you can find thousands on the web. I have them as the main source for my Hubbing Activity.. So I am conscience free.
A few websites that I use to get the free copyright images are :
You can always search for more galleries.
About the videos, with you tube is a little more complicated.
Normally they would say that technically any video that allows CODE to be embedded on a website, is allowing its videos to be shared, but some publishers do that , and do not necessarily know they are doing it, or simply they do it for their own personal use and then simply leave the code wide open for them selves, once they find someone using it they might simply file for COPYRIGHT issues and have the video removed. Using the code to have videos placed on your website could be considered ok, but if you don't want the videos to disappear all of the sudden , you should contact the Video Owner. You can't ask You Tube about the videos you want to you, as they will say to you that all content uploaded is the responsibility of the publishers him self. So You Tube will simply tell you to contact the video owner to ask for permission.
You could of course use the videos on your website, and then all of the sudden have them removed for copyright violation, but then again that happens mostly on music and entertainment videos. For more information use the following links to help you understand better the best option for you.
Similar questions to yours on YouTube's Forums.
Again, always a pleasure.
List of the most common copyright youtube questions:
Good luck to you.
Always a pleasure