Good evening!

1. Would a wire with a current of 1370 be feasible? (Hint: think about a light bulb filament)
I'm not sure... divide 1370 by 110?

huh?

eg
500 Watt light bulb
i V = 500
i = 500/110 = about 5 amps and it gets very hot

You would actually need to go he other way, low resistance with a very fat wire, like a welding machine. In transmission applications you go up to many thousands of volts to lower the current thereby reducing the losses to heating the wire.
See
https://www.quora.com/How-many-volts-has-the-output-of-a-welding-machine
specifically
"All resistance welding machines, whether spot, projection or seam, rely on a short burst of very high current being delivered to the workpiece. In order to achieve this high current, a large step-down transformer is at the heart of all such machines. The open circuit output is typically around 10V with currents of 10,000A +. "
You can do about any current if you make the wire fat enough and do not run it very long.