How Many Valar?

[Inziladun]

This discussion probably belongs in its own thread, but oh well.

...it appears that the first five incarnations of Durin had no offspring, otherwise Durin's line would have begun with them.

I don't see why that must be the case. The family tree referred to shows the Line of the Dwarves of Erebor. Durin the Deathless is shown because he is the earliest descendant of them and all dwarves of the Line. Gimli, who supposedly set down this family tree, obviously could not include every person in the Line. So the next Durin he shows is Durin VI, who was noteworthy as the last king of Moria, then his son Náin I, then Thráin I who was the first King Under the Mountain. Perhaps there was simply nothing notable enough about Durins II through V to include them there.
I don't think it specifically says anywhere, but one would think all dwarves named Durin would be of Durin's line.
That's quick cos I have to go to work. I'll try to read up on it.