1)
When did he choose 3,000 men?
1.
Radak: It was when he was still at Gilgal, after renewal of his kingship.
2)
Where did Sha'ul make his residence?
1.
Malbim: Part of the time he was in Michmash, and part in Har Beis Kel. He put 1,000 men in each, for the king should not be alone even at a time of Shalom.
3)
Why did he send everyone home, except for 3,000 men?
1.
Malbim: The norm is to remain in the house for a year after starting a new matter, e.g. marrying a women, building a house (Devarim 20:7, 5), or rising to power. He did not plan to fight wars, rather, to oversee the nation first.