Can I import a scene and objects made with Illustrator or Photoshop files into Unity?

I have an entire design of a game, scenes and objects made with Illustrator / photo shop.
All scene layout, buttons, instruments, background, colors, etc. should be kept as designed in a 2D-design. 8673-dual_compass_left.jpg

Can I import a .psd-file or any other adobe-format into unity?

Yes, Unity will import PSD files.

You may carry out this actions by using of how to fix adobe illustator tool problem

Read this item http://www.fixadobeillustratorproblems.fixillustrator.com/ to know how to do it