First bug: When you open “Add, remove modules” dialog, it ignores entered before custom <context-root> for web modules. As result if you press OK, it will rewrite application.xml replacing all <context-root> by its default values.
MyEclipse generates the application.xml file as a convenience. While you can certainly specify custom context roots, you should do this by entering them in the J2EE modules dialog that can be accessed by right-clicking on your EAR project and selecting MyEclipse > Add/Remove Modules…
So, this isn’t a bug it’s truly a feature.
Second bug:
I added a custom externat task to my application project. As result it adds “.externalToolBuilders” folder to the ear. It shouldn’t be there.
MyEclipse doesn’t add this folder, Eclipse does. The external tools need a temp area to work in so Eclipse provides one in this way. If you don’t want to see it, you can filter it in the Package Explorer view.