Create task in case via REST API

I have few questions about task creation on an already active caseInstance using REST API.
while looking at the camunda REST API documentation I have found this service which could help me
create task api.
But there are some things that aren’t specified and that I’m wondering about:
-Is it possible to select which type of task to create ? for example I would like to create a caseTask ! Which type of task is created by default ?
-Is it possible to assign a TaskListener to a task created via this service ?

To give an idea about the context, I want the user to be able to create a subtask that delegates work to another user at any task level present in my CMMN.

For creating case task, refer this link.