I don't think so... I think the transmission need electric power to engage.
The hood should still open when the battery is dead
Battery could be dead , or a poor cable connection to the battery
In the case of my 2003 Expedition, it turned out to be a bad starter motor after 55K miles.
Something is pulling power from the battery when the car is sitting idle. Check under hood, trunk, glove box lights, etc. Also can be a stuck relay. A battery may also appear good and have a dead cell. Have it tested.
battery is dead
manualy
Remove battery cover and connect charger to side post battery.
Check battery, charge it or change it. Dead battery.
For an external GPS, yes, assuming that battery is not also dead.
no
Your alternator is dead!
Battery is probably dead.