Let $M$ be a manifold and $k$ be a positive integer. Let $F(M,k)$ be the $k$-th ordered configuration space over $M$, consisting of all ordered $k$-tuples of distinct points in $M$. Let $\Sigma_k$ be the symmetric group on $k$-letters. Let $F(M,k)/\Sigma_k$ be the $k$-th unordered configuration space over $M$, consisting of all unordered $k$-tuples of distinct points in $M$.
Question 1: Let $p$ be an odd prime. Are there any references/results about the homology module $$ H_*(F(\mathbb{R}P^2,p)/\Sigma_p;\mathbb{Z}_p)? $$
My attempt: I search online and find that in the paper ON THE HOMOLOGY OF CONFIGURATION SPACES, C.F. Bodigheimer, F. Cohen and L. Taylor, 1989 Theorem C, we can obtain the homology module $$ H_*(F(\mathbb{R}P^2,p)/\Sigma_p;\mathbb{Z}_p(-1)) $$ of the chain complex $$ S_*(F(\mathbb{R}P^2,p))\otimes _{\Sigma_p}\mathbb{Z}_p(-1) $$ where $S_*$ is the singular chain complex and $\mathbb{Z}_p(-1)$ is the $\Sigma_p$-module $\mathbb{Z}_p$ with $\Sigma_p$-action given by $$\pi(1)=(-1)^{\text{sign}(\pi)}$$ for any $\pi\in\Sigma_p$.
Question 2: If $$ H_j(F(\mathbb{R}P^2,p)/\Sigma_p;\mathbb{Z}_p(-1))=0, $$ can we conclude $$ H_j(F(\mathbb{R}P^2,p)/\Sigma_p;\mathbb{Z}_p )=0? $$
