1)
What is the meaning of "Sigar"?
1.
Radak: He handed over the people and gave them into our hands. [Even though the verse does not say 'into our hands',] perhaps the prefix Beis in "bA'doni ha'Melech" is in place of two 1 .
2.
Malbim: David's men overpowered them.
1
I.e. as it says also 'b'Yadecha' (PF).
2)
Why didn't he say 'Hashem judged [the king] from his enemies', like he planned to say above (verse 19)?
1.
Malbim: This would hint to the death of Avshalom