I would like to apply the usual 'functoriality properties' of the perverse $t$-structure to torsion (constructible complexes of) sheaves (I am in the algebraic setting, so these are etale sheaves, but probably the difference from the 'topological case' is not very large here) i.e. I want to use the corresponding left and right $t$-exactnesses of $f_\ast$, $f^\ast$, $f_!$ and $f^!$ when $f$ is smooth or affine; constant sheaf over a local complete intersection variety (shifted by the dimension) is perverse; etc. It seems that there are two possibilities.

Reduce the situation to $\mathbb{Z}/l\mathbb{Z}$-sheaves (and consider the corresponding derived categories). Will the 'usual' properties of the perverse $t$-structure (for $\mathbb{Q}$ or $\mathbb{Q}_l$-sheaves) hold in this setting?

Consider arbitrary torsion sheaves and use only those properties of the 'obvious perverse' $t$-structure that are still true in this setting (cf. sections 3.3 and 4.1 of BBD).

My questions are:

Are the properties of $\mathbb{Z}/l\mathbb{Z}$-sheaves really parallel to those of $\mathbb{Q}_l$-ones?

What are the most appropriate references for possibilities 1 and 2?