Reuven and Gad did not request the land on the east of the yarden until after it had been conquered. See Matos 32:2 which has them asking Moshe and Elazar Hacohen (after the death of Aharon in the fortieth year). In any case, they were still considered as having received a nachalah with the others as it had been conquered and made part of the land.
The descendants of Gad and the descendants of Reuben came, and they
spoke to Moses and to Eleazar the kohen and to the princes of the
The Leviyim had replaced the bechorim immediately after the sin of the Golden Calf. By the time of the spies, the Mishkan had been built, Aharon had become the Kohen Gadol, and the Leviyim had been assigned to the work of the Mishkan. Note that in the census of Bamidbar 1:1 the Leviim were already not counted to get land and be in the army. They were counted separately in order to work in the Mishkan.
The spies sent in Shlach 13:2 were sent as the equivalent of a congressional junket with important men of the tribes. Each of them was sent as a representative of his tribe.
"Send out for yourself men who will scout the Land of Canaan, which I
am giving to the children of Israel. You shall send one man each for
his father's tribe; each one shall be a chieftain in their midst."
Rav Hirsch translates this as
"every one a prominent one among them"
On the other hand, Yehoshua sent Pinchas and Calev as actually spies on a secret mission. They were the equivalent of a Mossad team and were sent to report back to Yehoshua himself as the Bnai Yisrael were going to go no matter what.
The crying was done in the privacy of the tents of the individual tribes. As a result, there was nothing that the Leviim could have done. This is similar to the way that the Leviim could not rise up against the golden calf until after Moshe Rabbeinu had returned.
Since the punishment of the 40 years in the midbar was applied to everyone, no matter whether they took part in the rebellion or not, then the Leviim also mourned on Tish'a B'Av. Also, this day is set up as the mourning day for all the things that have occurred to use throughout our history.
We see that even though the women did not receive the punishment of death during the next 38 years, they still mourn.