12 volt battery, which is what you are connecting the jumpers to, is used to run all the electronics. If it is dead the high voltage traction battery, which actually starts the car and engine, will not do so. If your traction battery is dead, there is nothing you can do to charge it. It would need to be towed to the dealership where the proper charging can be done. Which is why the car's computer system will not let you deplete it.
Maybe not.
Page 167 of the owners manual:
"What should I do if the vehicle runs out
of fuel and the high voltage battery is
out of charge?
Refuel and start your vehicle normally.
The engine will recharge the high
voltage battery."
I cannot say for sure, am just going by the owners guide for Maverick. Ford does change things up.
For example, in first gen Escape Hybrids there is a switch in the lower left foot well, behind a little plastic door. If all the batteries go dead (and yes, I mean totally dead) connect your jumpers, press the button and it will flash. When it is done flashing the 'jump' will have recharged the hybrid battery enough to run the system. Start the vehicle as normal and let the batteries charge from the engine. I have done this many times on very dead vehicles.
If you don't press that button you can charge or change the 12v battery and the engine will start and stop immediately with the "please stop safely now" message displayed in the dash, which is kind of funny because you're not going anywhere.
Ford got rid of this button on newer hybrids. I have to think because it is an automated process once you connect the jumper cables and it sees a good 12v.
If your hybrid battery is actually failed, then jumping will not work, obviously.