If $(\mathcal{C},W)$ is a category with weak equivalences then we may naturally form its Dwyer-Kan simplicial localisation $L(\mathcal{C}, W)$. This is a simplicial category which naturally gives a simplicial enrichment of the usual 1-categorical localisation $\mathcal{C}[W^{-1}]$. I have two questions:

Is the $\infty$-category associated to $(\mathcal{C}, W)$ the simplicial nerve of a fibrant replacent of $L(\mathcal{C}, W)$?

Is it actually true that $L(\mathcal{C}, W)$ is a fibrant simplicial category itself, that is all hom-spaces are $\infty$-groupoids?