There are no general settings for searching inside apps. The Spotlight Search settings are for the search page (left most of your screens). To get to it swipe left until you get the search field, or tap the home button once to get to the first app page, then again to go to the search page.
The settings for Spotlight are Settings >> General >> Spotlight Search. There you can see the things that can be searched for. You can turn some of them off, but there is no way to add anything that is not already there.
To search a web page while in Safari, go ahead and enter the search word(s) in the Google Search field, then scroll to the bottom of the sugestions that pop up. At the bottom you'll see on or more 'Local' search suggestions (including the word(s) you entered) tap on that to highlight all the matches on the current web page. A small tool bar will appear to let you move to the previous and next matches.
Unless the Democrat Gazette Newspaper app has a search function built in, you are out of luck. As I said earlier, there is no general search function that will work inside the apps. It is up to the developer to provide that function.
