Why does it say "la'Menatze'ach bi'Neginos"?
Refer to 4:1:1:1-3 and the notes there.
What is "ha'Sheminis"?
Rashi (fast Erchin 13b): It is a harp of eight strings. We find also "Ploni u'Vanav Al ha'Sheminis Lenatze'ach" (Divrei ha'Yamim I, 15:21).
Radak (from Menachos 43b): It refers to Bris Milah, which was give [to be done] on the eighth day 1 .
Radak: This is far [from the simple meaning].
Why did David compose this Mizmor?
Radak #1: Perhaps it is when he was ill. Malbim - it was after the episode of Bas Sheva. It was a long, severe illness. He prayed for it (verses 2-7). Also his enemies hated and embittered him at the time. This pained him more than the illness (verses 7-11). The Mizmor discusses two enemies that besiege man. (a) The enemy that clings to him from his birth - the natures of his body and its fluids that rise against him to make him ill and kill him. (b) The external enemies, i.e. other people.
Radak #2: Perhaps it is for anyone crushed due to illnesses. David composed many Mizmorim to be available for anyone to pray. I lean to explain like this.
Radak #3: Some say that it is about exile. Yisrael in Galus are like ill, crushed people.
