Accepted answer
Gentle swirling dissolves a lyophilised cake far better than vigorous shaking, which causes aeration and aggregation.
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.
Number of stopper piercings matters less than the gauge doing the piercing.
The general principle — that peptides adsorb and denature at air–liquid and solid–liquid interfaces — is standard formulation science.
The caveat is that this is not a recommendation to administer anything. Research-use-only material is not approved for human use.
The practical summary: fine gauge, gentle swirl, diluent down the wall, room temperature before drawing, and check the syringe scale.