Subset sum with many targets
For what regards point 3:  the problem remains NP-complete: 


if $m$ is a parameter, then it is simply a generalization of SUBSET SUM;
if $m$ is fixed, then given an instance of SUBSET SUM, simply multiply every $a_i$ and the target sum $B$ by $p = 2^k$ s.t. $2^k&gt;m(m+1)/2$ and set $m$ target integers in this way: 


$G = \{ b_1=B,b_2=a_1+1,b_3=a_1+2,...,b_m=a_1+(m−1)\}$.

In both cases the problem remains solvable in pseudo-polynomial time.

For what regards point 2) you can find some information related to the density analysis for the ("simpler") SUBSET-SUM problem (it is usually defined in terms of $n/m$ where  $n$ is the number of elements of the input set and $m$ is its maximum);  e.g.: O'Neil, Thomas E. "On Clustering in the Subset Sum Problem." Proceedings of the 44th Midwest Instruction and Computing Symposium (Duluth, MN, 2011).