Why did Amalek attack Tziklag?
Radak: They investigated, and found that David took the spoils [of the places he raided] to there. Even though David did not leave anyone alive, Amalek asked the neighbors.
Who was left from Amalek? Sha?ul killed all of them less than two years ago!
Refer to 28:18;1.1:1-3.
What is "Negev"?
Radak citing Targum Yonasan, Malbim: It is the south. It is Samuch, but [what it is Samuch to] is omitted. Below (verse 14) it says "Negev ha'Kereisi" and "Negev Kalev."
Radak: It is the name of a city. We find "b'Ramos Negev" (verse 27). My first Perush is primary (refer to 30:1:2:1).
In what way did they strike Tziklag?
Radak, Malbim: It says (verse 2) that they did not kill anyone! Rather, they destroyed the city and burned it. "Va'Yaku" is a figure of speech for destroying the structure, like it says "va'Yerapei Es Mizbach Hashem" (Melachim 1 18:30), "v'Yo'av Yechayeh Es She'ar ha'Ir 1 " (Divrei ha'Yamim 1 11:18).
It does not refer to keeping the people alive, rather, to strengthening the wall (Rashi there).