Why did Nasan take action more than the others?
Radak: He prophesied that Shlomo will reign after David (Shmuel I, 22:9).
How did Nasan persuade Bas Sheva to go to David?
Malbim: (a) Do not say that you can wait. Adoniyahu already reigns! (b) Do not say that it is too late. David does not know. When he finds out, he will make Shlomo king! (c) Do not say that this is mere pursuit of honor and authority, and it is worth striving for it. "You will save yourself and Shlomo" (verse 12) - after Adoniyahu is king, he will kill you and Shlomo, for he knows that David wanted to make him king!
Why did Nasan send Bas Sheva, and not simply go himself?
Radak (15): Avishag lied in David's bosom on the bed with him. It would be improper for someone else to enter, but David's wife may enter his bedroom.
How did Nasan know that David did not know?
Radak: If he knew, he would protest, for he knew the prophecy that Shlomo will reign [after him].
