1)
Why did he say that she should request kingship for him?
1.
Rashi: Once he uses the scepter [or anything] of the king, this is the beginning of kingship.
2.
Malbim: You mentioned that kingship was proper for him, since he is my older brother - if so, request kingship for him!
2)
Why did he mention that Adoniyahu has Evyasar and Yo'av?
1.
Radak based on Targum Yonasan: Shlomo assumed that Yo'av and Evyasar counseled Adoniyahu to request Avishag.
2.
Malbim: You mentioned that kingship was proper for him, since Yisrael turned to him [to be their king], i.e. Evyasar and Yo'av - if so, request kingship for him, for that is what they wanted, and not Avishag!
