Why did they come to greet David?
Radak: The saw David and his men coming.
Why does it say "va'Yigash David Es ha'Am"?
Radak: It is as if it says El ha'Am. This is like "v'Her'ah Es ha'Kohen" (Vayikra 13:49), "Es Mi Higadta Milin" (Iyov 26:4). I.e. he came close to them and greeted them.
Targum Yonasan: He encountered the nation. Radak - some texts of Yonason say 'he came close to them.'
Malbim: He approached him with love. Es shows that he drew them close to himself, affectionately, to show that he does not resent that they did not come with him.
Why did he ask about their Shalom?
Malbim: They [did not go with him] because they were weary, therefore he asked about their health.