Disclaimer: I work for Google (though not Search), but this is merely my personal opinion.
With that said, I find Catholic Answers to appear a lot. It helps if I’m specifying that I want a Catholic position, and EWTN is probably the most common of all Catholic websites, but CA and CAF still come up enough that for a while I only knew of the site through Google searches.
Did any one tried to conduct research on the integrity and truthfulness of Google in the presentation of information?
I’m not aware of any hard research on actual statistics, and that would also be hard to do. If someone could get an assessment on how accurate the top sources are, then certainly Google would already be providing entirely reliable results, since they’d know how to do that. At best, you might be able to target a very limited subject, like results on an election during that election. However, I’m pretty sure that, in a general sense, the ones with the best numbers on Google’s reliability are the Search team, since they’re the ones bugs get sent to.
With that said, Google serves more as a portal to information, not a source itself. It’s there to make the world’s information available to you, and it tries to present the best* sources as early as possible, but you still need to be able to employ basic research principles, like critically reading multiple sources.
* And note that “best” doesn’t necessarily mean agreeable to you. I don’t know exactly how it works, but my guess is that for anything that doesn’t have a clear-cut answer, they’d try to provide the best sources for research, and that might include sources you disagree with. But at the end of the day, there’s absolutely no algorithm currently existing that can answer questions like, “Is God real?”
Is there not discrimination against Christians and religion in general in presenting truthful information in search engines?
No, at least not intentionally, and from what I’ve seen, they’d actually try to find ways to make Search more useful to Christians.
The very premise itself barely makes any sense. Google is a company that’s all about number of users and prides itself on having multiple billion-user products. It’s also the way that they make money. Given that, do you really think they’d want to alienate a religion that has over 1 billion followers among its largest branch alone?
If you remember the fruitful forum discussion of past years, and for example you decided to see if it is indexed in the top of Google?
In my experience, Google tends to aggressively prefer more recent results. The assumption isn’t without merit, but it does cause a disadvantage in that queries for stuff too old require a bit more work to get right, like explicitly filtering down to a certain time range, which Google supports.
Forums might also be a bit worse off since forums are generally not as reliable as primary sources or even more “official” third-party sources.