What is "Giv'as ha'Elokim"?
Rashi, based on Targum Yonasan: It is Giv'as Kiryas Ye'arim; now, Aron ha'Elokim was there.
What are "Netzivei Pelishtim"?
Rashi: They are officers appointed over Yisrael. Pelishtim subjugated Yisrael, and appointed Netzivim in cities of Yisrael. Radak - someone appointed over something is called Netziv.
Malbim: This hints that when he encounters the G-dly Nevi'im, he will merit to subdue the Pelishtim, like it says "va'Yach Yehonason Es Netziv ha'Pelishtim Asher b'Geva" (13:3).
What is "Chavel Nevi'im"?
Rashi citing Targum Yonasan: It is a company of Sofrim. Similarly, "Chevlei She'ol Sabuni" (Shmuel 2:22:6), Yonason translates as 'Mashiryas Rashi'in Akfuni.' Radak - Sofrim is Talmidim. These were Bnei ha'Nevi'im, Talmidim of the big Nevi'im from Eli until David, i.e. Elkanah, Shmuel, Gad, Nasan, Asaf, Heiman and Yedusun.
What is the significance of the Chavel Nevi'im?
Malbim (5,6): This is the third caste. They left the level of people, and became G-dly. They cast off bodily matters and engage only in spirituality and Divinity. Their company will 'feed' you your spiritual needs.
Why were the instruments playing in front of them?
Malbim: It was to try to arouse the G-dly soul until Ru'ach Nevu'ah will rest on it. Radak (from Shabbos 30b) - Ru'ach ha'Kodesh dwells only amidst Simchah.
Were they having prophecy?
Radak: Yonason translates 'they were praising.' I.e. their prophecy was songs and praises of Hashem via Ru'ach ha'Kodesh.