When you create zaps all the same restrictions are used as in Metatask itself. For example, if you are not a "Process starter" for a given template - you will not see this template in a list of available templates when configuring "Start a new process" action.
Administrators has access to any triggers and actions for all processes.
Process Managers have access to any triggers and actions for processes managed by them.
"Start a new process" action
Starts a new process from a template.
To use this action you should be a Process starter for a template you are going to use to start new processes. If you need to set some form fields' values you also will need to have permissions for viewing and editing these fields. In this case you should be a Process manager (you will have full access to all form fields) or candidate assignee of some task.
"Complete the task" action
Fills in form fields and marks a task as completed.
To use this action in your zaps you should have access to a task and process template as Process manager or administrator.
"Add New Comment" action
Adds a new comment to a task.
To use this action in your zaps you should have access to a task and process template as Process manager or administrator.
"Find a Process" search action
Find a process by a value of a form field.
To use this action in your zaps you should have access to a task and process template as Process manager or Administrator.
"Process Completed" trigger
Triggers when a process is marked as completed.
To use this trigger in your zaps you should be configured as a "Process starter" in the template used to start processes you want your trigger to work with. If you need to get some data out of completed process' data form you also need to be a "Process manager" of these processes or an assignee of some tasks in it.
"Task Created" trigger
Triggers when a task is created. It returns task's data form, due date and other task details.
To use this trigger in your zaps you should have access to a process template as Process manager or administrator.
"Task Completed" trigger
Triggers when a task is marked as completed.
To use this trigger in your zaps you should have access to a task, as a minimum you should be able to view it.
If you are a "Process manager" of a process or an assignee of a task you can use this trigger and use form data.
If you are "Process starter" you can use this trigger but you will not have access to a form data.