For requests - Yes, you can send notifications based on the purpose from mainly two ways, (1) workflow notifications and (2) Field value change notification.
The workflow notifications you can configure in the individual workflow step, e.g. when a step becomes eligible for a user or when a step is completed, etc.
The field value change notification you can configure from the request type > notifications tab.
Similarly for tasks, you can setup in workplan template or directly on the workplan or summary task or individual task. If you have a specific task on which notification needs to be sent, then you may setup notification on such task by adding the task in the workplan template itself (or you may already have such task in the workplan template).