1) You will need to do this manually. Dragging and dropping the web application artifacts into the correct location in MyEclipse.
2) You can do this two ways. 1 from the File > Export menu, and one using the Deployment tool from the toolbar.
MyEclipse won’t support putting the source code in the WAR by default, but you can make your source and bin dir both /WebRoot/WEB-INF/classes and just leave it there, although this is considered bad practice. If you need to share the project with someone else, it’s preferred to either put the project in source control somewhere, or simply use File > Export > Archive feature to export the project to an archive and send it to your co-worker.