It's somewhat a matter of preference, but I aim for 20 units as a good dose volume, so for your 10mg vial that would mean using 1ml of water. That works well since you have a 1ml syringe for the reconstitution. You can draw a little extra, like 103 units, to account for losses in the dead space when dosing from the vial, so you don't run short on the last dose. Multiple draws aren't necessary since 1ml is sufficient. For unlabeled BAC water, if you can get more, I'd discard the remainder rather than save it. Try to get better quality BAC next time. I don't worry about how the vials are oriented in the fridge.
Reconstituting isn't a problem for me, but I have a few questions for the more experienced people here. I'm thinking of ordering 10mg and mixing it with 2ml of BAC water to get five 2mg doses, drawing 40 units from a 1ml syringe. If my syringe is only 1ml, can I add the 2ml in two separate 1ml draws using the same syringe, or do I need a larger one for everything at once? Should I discard the leftover 1ml of BAC water, or is it okay to save for the next vial? After mixing, can I lay the vial on its side in the fridge, or must it stay upright?