how long can an external hard disk be kept on without turning off the power?

Question

is there any damage to the hard disk if it is kept on for long hours, as it gets very hot hot?

Answer 1

Probably a design flaw. Don't risk a fire. Keep it away from paper and plastic.
Externals usually are meant for portability or backup of data. So - add an internal drive if you can.
Hard drives generally last longer if kept running rather than powering up and down all the time, but the heat might also cause its life to be shortened.