The rubber stopper at the end is very tight. No water is going to leak out. If you're not comfortable holding it vertically than lay it on its side. I do it with my 12mg cartridge and never lost any water. I hold it straight up so the air comes to the top of the front chamber while the bottom of the same chamber will have the puck and water doing its thing. Just remember to have a pin in the top to release pressure. If you don't, the water will only go half way in the front chamber and the increased pressure in the front chamber will cause the gray stopper to create suction and part of the reconstituted protein will end up in the rear chamber, exactly where it's not supposed to be.
You can use the same syringe. I don't see why not.