1)
What is "Nish'ol Nish'al"?
1.
Rashi: He asked permission.
2.
Malbim: Others, i.e. his family, asked him [to come]. He did not ask the king himself (rather, me) because he needed Larutz (hurry). It is for the entire family, therefore they want him to come.
2)
What is "Zevach ha'Yamim"?
1.
Rashi: It is an annual family Zevach at this time of year. Radak - they offer and eat Shelamim, like it says about Elkanah "Lizbo'ach Es Zevach ha'Yamim" (1:21).