I have one small server on EC2.
Let's say I cURL facebook.com. What IP will facebook see as the "client address"?
Is it random?
If you haven't assigned an elastic IP to your instance, the IP will change every time you reboot the instance, however it will not change upon every outgoing request.
To be more specific towards your question: No, the address will not be random, it will be taken from a pool of available addresses when your instance is started.
See http://docs.aws.amazon.com/AWSEC2/latest/UserGuide/using-instance-addressing.html for more info.
To see your external IP from the command line you can run:
curl ifconfig.me