1)
Why did they seek David?
1.
Radak: They wanted to fight with him. David then composed "Mizmor Lamah Ragshu Goyim" (Tehilim 2), for all Pelishtim gathered.
2.
Malbim: Until now, they thought that he has a Bris with Achish and fights against Malchus Sha'ul. Now that [all of Yisrael] accepted him as king, they wanted to see if he will be submissive to them and pay taxes.
2)
What is the Metzudah to which he went?
1.
Radak: It is a strong tower. It says "he descended", for the place was lower than Yerushalayim.
2.
Malbim: This is the fortress in Midbar Ma'on, where he went when he fled Sha'ul. It is close to Eretz Pelishtim.