Can Javascript in Java Web Application cope together?

Yep. Javascript makes sense.   If you had to only display diagrams, you could do the logic on server and send the diagram in a browser displayable format (svg or any image format), Since you say, user will be able to update the elements, the only option I see is using client side languages and frameworks. My suggestion is to find a good Javascript framework that supports MVC and make use of it to convert diagram attributes into a model and get it synced with server.

Javascript is primarily a client side, prototype scripting language, it has nothing to do with your Java EE environment. It communicates primarily with the browser and DOM, so any configuration would have to be on that side. That said, I would suggest you go for something like JQuery UI which provide a whole lot of plugins, that can be used, without having to write too much code.

of-corse, you can use Javascript in parallel with any other Server-Side language including Java. Javascript has nothing to do with server side languages, it communicates directly with DOM and Browser. As per your requirements it will be very useful to use Javascript for diagrams and other visualization. Use JSON encoded data for the Javascript data source

Javascript is good... But You can also use jquery... It provides plugins for diagrams etc.

Of course. You can use Java as a scalable server platform and access it via JavaScript. But in general they don't have anything to do with each other.