A java program can do anything just as long as you have to right API for the job. That is what you should focus on, not on the java language itself because Java is no more than that: a programming language. The standard SDK has no support for playback of video that I'm aware of, but there is always google to help you find a free/open source API that can do it.
The standard SDK does have the ImageIO class that can be used to load and save images, which gives you the capability to convert types. Gif, png and jpeg will all work out of the box (bmp will too if I'm not mistaken). Other than that there is the java advanced imaging API (JAI) that gives you the ability to transform images.
yes you could build that if you go and download the JMF (Java Media Framework). Unfortunatly, all your users will have to download it too because it is not part of J2SE. It will allow you to run many types of video as well as audio in both applets and applications. It does take a while to learn as well, however it is a sun API so it will be maintained, maybe even someday added to the J2SE (I hope). You can download it here...
http://java.sun.com/products/java-media/jmf/2.1.1/download.html