Is it default that arduino nano gets hot?

good morning,
however, problems with arduino remain

another arduino nano - i guessed it would be in order -
now does not communicate correctly with pc

i have read several articles in this forum - i.e. loop-back-test
there is no echo !
uploading fails the attempts 1-10 gave no success

just after connecting arduino pc only red on-Board-LED is on,
doing the success-less loop-back-test additionally the green on-Board-LED goes
and stays on

this behavior shows that perhaps not all is damaged (i hope)

how do you interpret this ?