1)
Of whose kingship was this the ninth year?
1.
Rashi (Melachim II, 25:1): It was of Tzidkiyah (Yirmeyah 39:1). Radak (Melachim II, 25:1) - it was Nebuchadnetzar's 17th year.
2)
What is "Dayek"?
1.
Rashi citing Targum Yonasan: Karkum (siege).
2.
Radak (Melachim II, 25:1): It is a wooden tower that they build against a city in order to conquer it.