Defending the honour of a Muslim

Q: The Hadith of Rasulullah Sallallahu alayhi wasallam states: "He who defends the honour of his (Muslim) brother, Allah will secure his face against the Fire on the Day of Resurrection." [Jami al-Tirmidhi]

1. I have been in situations where Muslims (especially Ulama) are defamed. This sometimes happens in face to face conversations and sometimes on social media. I feel that it is my duty to defend my Muslim brother. However, a person told me that if I do not know the background to the entire situation/incident, I should keep silent and I should not defend my Muslim brother.

I wish to ascertain whether or not I should defend my Muslim brother in such situations despite my insufficient knowledge of the entire background.

2. The person who told me this explains that if I do defend my Muslim brother in such a situation without full knowledge of the background, I am indirectly defaming and doubting the person who passed on the information. Is this the correct understanding?

Removing impurity from a touch screen phone

Q: I have a question regarding impurity and touch screen phones. I would like to know how invisible impurity such as urine traces or other invisible impurity may be removed from a cellphone as it cannot be washed as it would be ruined. Would wiping the dry invisible impurity with a dry cloth remove it from the smooth surface of a phone? Or how about a wet cloth that is wetted with isopropyl alcohol (as this does not harm the phone)?

Keeping textbooks containing words that may affect one's beliefs

Q: I am a science student and I have a bunch of math textbooks. These are strictly math textbooks as I understand. In one of the books, the author mentions solving equations in their multiple variable "incarnations". I assume the author means "form" because there is no religious meaning here as far as I can tell. In a different book, the author tells a short biography of a mathematician who was also an astrologer. The presence of such words disturbs me. I would like to know if there is something wrong with me continuing to read these textbooks and can I keep them or not.