Qasual ; When the bike is fully warm, adjust the idle on the right side of the bike behind the cylinder head (There should be a little turn knob that is very visible) . Why I recommend this is because the idle may be set to low when the bike is starting but it is running strong because of the use of a choke and after slightly warming up you possibly started riding until it is fully warm. So when it is warm you pop her in neutral and the GZ starts to cut out, in the fully warm state adjust the idle and you should be good to go.
The second question; You should have it in the fuel position, also get familiar with where the knob is and where the other positions are. When you are losing power or cutting out due to low fuel you will have to reach down and switch it to reserve. Prime is only used when the bike (Or I would say Carburetor) is out of fuel OR the bike has been stored for a lengthy amount of time and switched back to 'FUEL' before start up unless necessary you can keep it on prime.