I can give you a partial answer to question 1, which you may already be aware of if you're familiar with Pedersen's "C*-algebras and their automorphism groups". Specifically, if $A\subseteq A^{**}$, i.e. if we are considering the universal representation of $A$, and if $A$ is either unital or separable then you do indeed have $(A_\mathrm{sa}^m)^m=A_\mathrm{sa}^m=\overline{A_\mathrm{sa}^m}(=$ norm closure of $A_\mathrm{sa}^m$). For if $A$ is unital then, by Pedersen 3.11.7, $A_\mathrm{sa}^m=\overline{A_\mathrm{sa}^m}$, while if $A$ is separable then we again have $A_\mathrm{sa}^m=\overline{A_\mathrm{sa}^m}$, by Corollary 3.25(a) of Lawrence G. Brown's "Semicontinuity and Multipliers of C*-algebras". By Pedersen 3.11.5, $\overline{A_\mathrm{sa}^m}$ consists precisely of those $x\in A^{**}_\mathrm{sa}$ that are lower semicontinuous on $Q=A^{*1}_+$, which are immediately seen to be closed under taking supremums of bounded increasing nets.

If we consider $A$ with its atomic representation instead, then the above remarks still apply, as there is then a normal morphism $\pi$ from $A^{**}$ onto $A''$ which is faithful on $A_\mathrm{sa}^m$, by Pedersen 4.3.13 and 4.3.15. Arbitrary representations can be faithful on $A$ but not on $A^m_\mathrm{sa}$, although in general you might perhaps try to use the predual $A''_*$ of $A''$, in the topology induced by $A$, as a replacement for $A^*$ with the weak* topology. The only problem is that $A''^1_{*+}$ may not be compact in this topology so you would have to somehow adjust the proof of Pedersen 3.11.2, on which 3.11.5 relies.

Incidentally, it is a problem of Akemann and Pedersen from 1973 (still open as of 2014 according to Brown) whether $A_\mathrm{sa}^m=\overline{A_\mathrm{sa}^m}$ for arbitrary $A$ in its universal representation, so if you or Nik have a counterexample it would be quite important.