The topic of operating apps/sites on Shabbat is complex, an entire book (Commerce and Shabbos) was written on it by R Yosef Y Kushner.
In general it is permitted to write an app that will maybe be used by Jews on Shabbat (and there are thousands like this of course). R Shlomo Aviner writes that, regarding "Do not place a stumbling block", if one is uncertain that the person will transgress the Halachah, we are "tolim" (literally "hanging" on the assumption) that he will not violate it (Mishnah Gittin 5:9) (see bottom of here).
We also know that
- some sites operated by religious Jews (e.g., B&H Photo) are operating on Shabbat with the commerce function disabled (i.e., you can browse but not buy)
- some sites operated by religious Jews (e.g., artscroll) shut down entirely
R Kushner explicitly addresses a number of relevant topics for your app
- Operating an e-commerce website on Shabbat (p. 183): he writes that according to the overwhelming majority of poskim, a Jewish-owned website may remain open on Shabbat, for reasons similar to those explained here (which would explain B&H)
- Profiting from online advertising on Shabbat (p. 200): permitted if the earnings generated from ads run on Shabbat are received by the Jewish owner together with the money earned from advertising during the weeks
- Operating a website used by a majority of Jews (p. 190): he writes that it would be better to avoid leaving the website open on Shabbat (which would explain artscroll) - I understand this is not your case but wanted to be complete
So there are likely to be poskim who will permit or prohibit based on the specifics of the case. But you really need to speak to a competent rav to review the specifics and get a personal ruling. The above might serve as a helpful review of some of the sources.
Regarding lashon hara on the Internet, there is a book for this as well :-> (but I don't have it), this review (bottom) mentions it explicitly addresses issues relevant to your question.
Since newspapers are definitely constrained by the laws of lashon hara (see e.g., bottom of here), it stands to reason you will need rabbinic guidance on your app as well.
R Dovid Genish writes
Newspapers certainly contain much lashon hara, and as the Chofetz
Chaim makes clear, the prohibition includes not writing negatively
about other individuals, groups or communities. Az Nidberu (14:64)
discusses the issue of liability – is it the journalist who has
transgressed lashon hara or the publisher/vendor?
His conclusion is that the writer is certainly guilty, for even though
at the time of writing he did not tell anyone his lashon hara, once
his words are published he has transgressed retroactively. On the
other hand, the publisher or vendor is by and large not liable since
he has no intention to spread lashon hara – he merely earns his
livelihood by selling newspapers, but does not specifically intend to
damage others. Nevertheless, he recommends that one should stay as far away from such newspapers as possible.
Last, halachayomit writes in a way that would make it challenging to automatically republish articles from "non-kosher sources"
I also contacted Arutz-7, a radio station here in Israel. One of the
founders of this station is a Rosh Yeshiva (dean of a Yeshiva), and I
believe that they sincerely try to avoid lashon hara. The following is
the reply that I received from [them]
Rabbi Zalman Melamed - the Rosh Yeshiva of Yeshivat Beit El, Rabbi of
Beit El, and one of the founders of Arutz-7 - is the rabbinic
authority of Arutz-7. His guiding principle is, first of all, that
something that is already known (public knowledge) can not always be
publicized - as publicizing it further is at least avak lashon hara (a
statement which is not lashon hara itself, but will cause lashon hara
to be spoken).
Equally obviously, the above rules out all sorts of gossip columns,
which have absolutely no place in a Torah publication. Similarly,
crime stories usually should not have any names mentioned. Even
political figures, who are often justifiably criticized based on the
above principle of "benefit to the public," should not be mentioned by
name in cases that can bring no such benefit - such as how many times
he was divorced, or the like. There have been several cases when we
have specifically left out names, even though in a "normal" newspaper
they would have been mentioned totally matter-of factly".