Try Having your alternator checked at a local Auto Zone or Napa. If it's not that it could be your starter.
No you do not need a battery, but the lights and horn will not work unless you have a battery installed, dead or not.
dead cell in the battery or something is on that is pulling power from the battery.
Check your battery connections. If they're tight and no corrosion is present, then your battery may be dead. Recharge or jump start the battery. Still clicking? Replace the starter.
starter, solonoid, ignition, battery. if it clicks when you turn the key then the battery is really dead or its the starter the battery could still be jumped if its the battery.
dead battery?
That could be the alternator or the battery. Try jump starting your car with another car's battery. If it still does not start, it is probably the alternator. If it starts, your battery is dead.
Dead battery?
check fuel pump
Sounds like a dead battery. You need the battery to start the car, but once it is running the engine runs completely off of the alternator (which also recharges the battery if the battery is still good).
Battery could be dead , or a poor cable connection to the battery
from a dead battery to working battery
For an external GPS, yes, assuming that battery is not also dead.