1)
What is the meaning of "Kol ha'Mamlachah"?
1.
Radak: It is any part of the kingship. The same applies to "Lo Sa'aseh Kol Melachah" (Shemos 20:10) and "Kol Chelev v'Chol Dam Lo Sochelu" (Vayikra 3:17) and similar verses. Malbim - it will be taken only from his sons.
2)
Why did Hashem say that he will make [Shlomo] a Nasi?
1.
Malbim: He will cease to be a Melech, who bequeaths his authority to his sons. He will be a Nasi, who does not bequeath his authority to his sons.