Is ghusl and making up the day obligatory for someone from whom an involuntary fluid was discharged while fasting after browsing a website about the manner of sexual intercourse, knowing that she cannot differentiate between semen (mani) and prostatic/pre-seminal fluid (madhiy), and she suffers from involuntary urination?

We advise you to stay away from anything that arouses desire. The fluid that came out of you could be maniyy (spermatic fluid) or madhy (pre-ejaculatory fluid). If it was maniyy, ghusl (ritual bath) is obligatory. If it was madhy, only cleansing the area and performing wudu' (ablution) are necessary. If you are uncertain and cannot distinguish between them, you may choose to assign it the ruling of one of them, or act according to the ruling of both, which is more cautious. Your fast is valid in all cases, because madhy does not invalidate the fast, and maniyy invalidates it only if its emission was intentional.