What is the ruling on abandoning prayer after the emission of fluid from the anus following a strike to the penis in self-defense, and is it permissible to perform ghusl or tayammum in this situation?

What happened with your friend's brother's wife appearing before you with a bare chest is likely a result of leniency in observing the Islamic regulations regarding entering upon women or being in seclusion with them. One must be cautious when entering upon women, for "the in-law is death." And no man should enter upon a woman whose husband is absent unless he is accompanied by one or two trustworthy men.

You did well in being keen to preserve your dignity and the dignity of your friend's family, but the fear of Allah and the awareness of His constant watch should have been a greater motivator for you to desist. You erred by striking your private parts, as this involves self-inflicted torment and harm to the body.

Your abandonment of prayer due to the fluid flowing from your anus is a greater mistake, as it is impermissible to delay prayer beyond its prescribed time without a legitimate Shar'i excuse. This fluid is likely inflammatory discharge; it should be washed off, and one should perform ablution (wudu') from it as it is a minor ritual impurity. Abandoning prayer for this reason is a sin for which repentance is obligatory, and you must make up for the missed prayers. If its discharge is continuous, it is considered " سلس" (incontinence), and its ruling is mentioned in related fatwas.