You can use tmux, there are many detailed introductions online. Just look it up and you’ll know, so I won’t go into details.

I don’t understand the meaning of the question.
If the running information is printed by the python file itself, then the subject can directly write the running information into a log file in the python file.
If it is system printing, you can use the redirection method to redirect the information output to the screen to a file.
The questioner can learn about Linux system redirection