Are faxes sent sequentially from one extension?

They will be on the queue and most probably sent sequentially.

As per I know, API calls are sequential and fax should be send one after another depending upon the number of times you called the API.

Until and unless you use any logic to make it parallel using coding, for example from a Java code you can call the APIs parallel 10 times or from a Mulesoft code I can call api 10 times with scatter gather coding, default should be sequential.