Strange behavior of REST API

I am testing Camunda REST API and have the following question.

As Camunda provides a REST API /task/create, I could create task by calling this endpoint. In this case, I get a row created in the ACT_RU_TASK table, but the fields, such as EXECUTION_ID_,
PROC_INST_ID_, PROC_DEF_ID_ are empty. So the task created with no association to a process definition? Why the API allows creating such tasks?

What would be the correct way of creating/initiating a process?

POST request to http://localhost:8080/engine-rest/engine/default/process-definition/key/invoice/start end point?

You can create tasks that are standalone and not related to a process. The endpoint you listed is the correct endpoint to start a process instance.

@StephenOTT What is the purpose of creating a standalone tasks, which are not associated with a process?