1x10-4 N HCl would work well for stock solution (~1mg/ml), which can be diluted to working concentration in the medium containing FBS or BSA at neutral pH. If an intermediate dilution is needed, use 1mg/ml BSA in H2O or PBS.

No, do not add DMSO to the solution. Dilute the supplied solution with BSA in PBS, if BSA does not interfere with whatever is it that you are going to do.