You can copy and paste with animations by selecting your elements (make sure they are all selected and you don't have any locked items) and then clicking Edit > Paste with animations.
If you have a scene with multiple layouts:
Select File > Export > Advanced Export, and select individual slices to export:
A quick way to preview your layouts is to Preview in Safari, and turn on 'Develop' in Safari's Advanced Preferences, and then type ⌘ + option + r, which gets you into 'Responsive Design Mode'. You can then adjust the width of the preview area to match your layout for testing.
Chrome also has a tool for that in its developer tools.