Is it obligatory to mention the source when publishing posts on a Facebook page, given that the original content may be modified, quoted, or have ideas added that contradict the author's intent, and does mentioning the source reduce the page's effectiveness, and what is the ruling on previous posts if this is [considered] unlawful?

It is permissible to transmit and quote, especially if it is not verbatim. This has become common practice in the books of jurists. If the websites retain intellectual property rights, then whatever is transmitted from them must be attributed. Al-Shawkani said: "It has always been the custom of authors that the latter comes and takes from the books of those who came before him, either abridging, clarifying, or objecting..."