Q: Can one believe all the abstract- and indexing-related information that is provided on a journal's home page?
Under each journal’s home page, they have a tab that specifies abstracting and indexing information. Can one believe that which is stated by these journals?
I believe you are referring to the About menu or page. On the About page, every journal provides information about the various databases in which it is indexed. By “abstracting information,” I guess you mean that when you search for articles in these journals or databases, search results show only the abstract of each article, based on which you decide to download and read the complete article.
To answer your question, you can believe or trust the journal and the information it provides if it is a quality journal, such as being owned by a reputed publisher, having an established history, featuring articles that are frequently cited, and having a high impact factor. (Note: Impact factor as a marker of journal quality has been much debated in recent times. If interested, you may learn more about this here.)
However, there are several bogus journals that have emerged in recent times to take advantage of the pressure to publish experienced by junior researchers. These have come to be known as predatory journals as they prey on unwary researchers. The good news is that there are several ways to identify these journals. To know more, you may refer to this resource: 10 Point checklist to identify predatory publishers
Finally, it’s great to note that you have an inquisitive, analytical, and critical mind. Those are among the many attributes of a successful researcher. So, more power to you!