1)
Why did Hashem call this day for crying
1.
Radak, Malbim: He called it via Nevi'im, before the punishment came, in order that they will cry
2)
Does crying apply to Hashem? It says "Hod v'Hadar Lefanav Oz v'Chedvah bi'Mkomo" (Divrei ha'Yamim I, 16:27)!
1.
Chagigah 5b: Normally, there is crying in front of Him in inner rooms 1 , but not in outer rooms. Churban Beis ha'Mikdash is an exception - even angels cried over it - "Hen Er'elam Tza'aku Chutzah Mal'achei Shalom Mar Yivkayun" (33:7).
1
Michtav me'Eliyahu (5, p.447): Hashem has all perfection. There cannot be an addition or detraction from Him. His Simchah or crying is only from the aspect of those who receive [influence from Him].