  Extending the main result of Part 1, in the first part of this paper we show
that every quiver Grassmannian of a representation of a quiver of extended
Dynkin type $D$ has a decomposition into affine spaces. In the case of real
root representations of small defect, the non-empty cells are in one-to-one
correspondence to certain, so called non-contradictory, subsets of the vertex
set of a fixed tree-shaped coefficient quiver. In the second part, we use this
characterization to determine the generating functions of the Euler
characteristics of the quiver Grassmannians (resp. $F$-polynomials). Along
these lines, we obtain explicit formulae for all cluster variables of cluster
algebras coming from quivers of extended Dynkin type $D$.
