Concretely, the distinction that resolves most of these questions is that bacteriostatic water suppresses microbial growth and does not sterilise anything. It buys you a multiple-withdrawal presentation; it does not make an unsterile preparation sterile, and it does not substitute for technique.
The order of operations matters: temperature first, then diluent measurement, then injection, then gentle dissolution, then labeling.
On re-freezing something that thawed in transit: if it arrived as a lyophilised solid that warmed but never got wet, re-freezing costs you nothing except the thermal cycle.
None of this is exotic. It is just the difference between doing it deliberately and doing it approximately.