Question: I say everything I hear to others around.
I'm not an animal, nor part of the human race.
I will, immediately, repeat after you;
But only if my tail is in place.
What am I?
Question: It runs and runs but can never flee.
It is often watched, yet never sees.
When long it brings boredom,
When short it brings fear.
What is it?
Answer: Time, which is often watched when you stare at a clock.
Question: Find the four digit number in which the first digit is one fourth of the last digit, the second digit is 6 times the first digit, and the third digit is the second digit plus 3.
Question: Riddle me this, Batman:
What is my name?
The Germans played
a cryptic game.
Answer: The Enigma machine.
The Germans used this machine in World War II. This is alluded to in the second part of the riddle. As to the first part, The Riddler's real name in the Batman universe is Edward Nygma, or E. Nygma, which is a play on the word "enigma". Both of these hints together point to the Enigma machine.
You can find online simulators of the machine and use them to send encrypted messages to your friends. When they ask how to solve it, you can give them this riddle as a hint. That's what I did. You do what you want.