I have an idea for a web app that will target to a specific audience and will collect news and blog articles, analyze them (for keywords, trending topics and more) and then display the article headlines on the website, along with links to the original article. Is it a violation of copyright to display headlines in this way?
So for the specific intellectual property issues, if this is central to your proposition then you must seek professional advice. This note isn't that, but it does reflect my practical experience in a similar space.
Ideally, you need to look at the directly stated terms and conditions of a site, and implicit terms (for instance, if there's a robots.txt file prohibiting spidering of some/all of a site, you have to take that into account; if there's an RSS feed then that implies a positive attitude).
then it's hard to see you're going to run into any serious problems.
If Google can do it, so can you. Google will copy the title of all web pages that don't have robots restrictions, including a snippet of a few lines of text.
IMO as long as you collect only headlines - No.
I do not know the answer, but I have seen a website that caught my attention and is aggregating titles + about 5 lines of articles: domaining.com This site is basically just aggregating blog posts as "news". So it seems possible.
Bloggers don't seem to mind: as I understand, they want to be on that site because of the traffic it brings.