I like the headlines from Spotlight Search, but I hate that fact it displays many sites that have paywalls (e.g., LA Times, NY Times, etc). Is there a way to tell iOS not to show certain sites in the headlines?
Unfortunately, no. Apple doesn't give us a way to adjust the news sources for spotlight search. There's rumors that it takes your preferences into consideration when you read and swipe-away articles in the News app, but I haven't seen that happen yet with my preferences.