Yes. It would.These are electrical circuits - where a "circuit" means a closed path. You must have a return path for the current in each of the interconnections.Just very basic electrical theory. If you connect a battery to a LED with only one wire, it will not light.
Yes grounds can and should be connected together.See this for a diagram illustration the point:-http://www.thebox.myzen.co.uk/Tutorial/Power_Supplies.html
i do have 2 GND don't i? One of the Arduino(USB) and one of the power supply from the Breadboard.