Display Hoogle results in app?

Can I in some manner display Google results in an app without violating any laws/rights?

It depends on what you are searching. Previously you could search the entire web and display results via their API. Now you can only search and display restyle that you pulled in yourself (your own sites, etc):

You can play around with it using the Free edition:

If you are scraping the results and displaying, then that’s a whole other situation.