Is this sign the same as 'relax'?
Yes, this sign is often used interchangeably with 'relax'. The context of your sentence and your facial expression will clarify whether you are telling someone to 'calm down' or simply talking about 'relaxing'.
Can I use just one hand for this sign?
While it's possible to use one hand in very casual, fast-paced conversation, using both hands is standard and makes the sign much clearer, especially when you want to emphasize the need to settle down.
How do I make the sign stronger if someone is very upset?
To show a stronger need to calm down, you can make the downward motion slightly more deliberate and pair it with a firmer, more serious facial expression, maintaining eye contact.