@finldyou can find more details on this feature in Pega Docs

• https://docs.pega.com/bundle/platform/page/platform/case-management/creating-tasks-optional-actions.html

Specifically, to your questions. 

• Recommendation - Child Case: The nature of your questions indicate the desire for more Case Management features, both now and probably more in the future. So I would look to be creating a generic case type to handle the "Adhoc tasks".  This doesn't need to be a complicated case, a label, description and dynamic SLA to track the case management features (like notifications). 
  • In addition, you'd get case features for "free" with a case:
    • Ability for multiple people to work on multiple tasks at the same time (adhoc assignments would not provide that benefit)
    • Child cases tab on your parent case (easily navigate between them)
    • Waiting for child cases from parent (to resolve)
    • Pulse (notes)
    • Attachments
    • Optional actions (against the task)
    • Stakeholders/Participants (tag people responsible or contributing)
    • Insights/Reporting on them
    • Collation of more data on creation 
  • On top of this, if you're using Constellation, you've already moved more towards the concept of requiring Cases to do processing (stateless UI). Another reason why, i like having a case.
• Extending Adhoc Tasks: The out of the box action "Adhoc Tasks", uses an Activity, which triggers an SLA and creates an assignment on the current case. The SLA is marked Extension, so the intent is for implementations to extend. The others are not final rules, but are probably left alone unless absolutely necessary - your project would have to make an informed decision if to override these, knowing it would add maintenance overhead if you update and pega modifies these. 
  • 
  • In additional to this, you'd have to look at creating rules on your cases to check these open assignments before closing. This isn't Out of the Box in the same way parent-child case relationships are managed, which is why I recommended that approach

I've used both approaches, and prefer the flexibility that recommended option provides but your project would need to assess which is the best route for you. 

Inspiration?

Infact, this is way one of our strategic apps deals with the scenario Pega Government - a case that can track any adhoc tasks > they have a feature called "Activity Plans" that allows you to create on the fly tasks, in a 3 level hierachy from any case type.

• https://docs.pega.com/bundle/pega-government-platform/page/pega-government-platform/implementation/activity-plan.html

Check it out for inspiration - not suggesting you replicate all of it, that is extensive, but it does show you what you can easily achieve with a case controlling this, instead of adhoc assignments