When does he bring Nedavah?
Rashi: It is during the six weekdays. Radak ? the verse already explained what he offers on Shabbos 1 , Rosh Chodesh and Mo'adim.
Why did Radak need a source that he is not offering Nedavos on Shabbos? He explains that many laws of Korbanos will change ? one might have thought that also this will be permitted to the Nasi. Malbim could hold that here discusses the days of Chinuch; Nedavos were offered on Shabbos in Chanukas ha'Mishkan. (PF)
Who opens the gate for him?
Radak: One of the gatekeepers.
Do they open the gate for him to enter through it?
Rashi: No. He does not enter the Heichal; he stands there, and Kohanim offer his Olah and Shelamim. He bows and leaves ? "Ka'asher Ya'aseh b'Yom ha'Shabbos"; on Shabbos, "v'Amad Al Mezuzas ha'Sha'ar v'Asu ha'Kohanim Es Olaso?" (2)
Radak: This is the eastern gate. It is normally closed during the week. They open it for him to offer a Korban (Malbim ? for his honor).
Why do they close the gate after he leaves? On Shabbos, they did not close it until the night (2)!
Rashi: On Shabbos, commoners bow at Pesach ha'Sha'ar, therefore they leave it open. On weekdays people do not normally come to bow, for everyone engages in his work 1 . Therefore, they close the gate after he leaves. Radak ? also on Rosh Chodesh, many are idle from work due to the Korban 2 , and will come to bow.
Shabbos 32b learns from Zecharyah 8:23 that in the future, everyone who is careful about Tzitzis will have 2800 slaves! Perhaps they will be busy overseeing their slaves. Malbim could explain that here discusses the days of Chinuch, and the verse discusses after the war of Gog and Magog. (PF)
I.e. Musaf Rosh Chodesh. Ideally, one should be present when his Korban is offered. Ma'amados are everyone's Sheluchim; it is as if they are present. Many will prefer to be there themselves. (PF)