I can at least answer your second question. I'll be a bit brief, but let me know if you need more details. Let $M$ be an oriented manifold and $M^{(r)}$ the configuration space as in your question. Then it follows from the Totaro spectral sequence, i.e. the Leray spectral sequence for $M^{(r)} \to M^r$, that the map $M^{(r)} \to M^r$ induces an isomorphism on $H^1(-,\mathbf Z)$ whenever $\dim(M) >2$ or when $M$ is a punctured surface of positive genus.

To see this use the exact sequence of low degree terms:
$$ 0 \to H^1(M^r,\mathbf Z) \to H^1(M^{(r)},\mathbf Z) \to E_2^{0,1} \to E_2^{2,0}$$
If $\dim(M)>2$ then $E_2^{0,1}=0$. When $\dim(M)=2$ we have $E_2^{0,1} = \mathbf Z^{n(n-1)/2}$ -- a copy of $\mathbf Z$ for each small diagonal -- which injects into $E_2^{2,0} = H^2(M^r,\mathbf Z)$ because each diagonal maps to a different Künneth component of the form $H^1(M,\mathbf Z) \otimes H^1(M,\mathbf Z)$ (the class of the diagonal in $H^1(M,\mathbf Z) \otimes H^1(M,\mathbf Z)$ is nonzero precisely when $g>0$). The result follows.