Integrate Tasks into Calendar (Google or local)

It would be really useful to have tasks integrated into the calendar in a similar way to how Google Calendar or Business Calendar for Android do it.

Tasks would have the following characteristics:
- Have date and time (like calendar events)
- Have zero duration, but show up in day view as a 30-minute block
- Have a reminder that fires at the time of the task
- Have a checkbox that allows to mark them done. When checked, the tasks title becomes struck through.
- If not marked done on their day, they would accumulate in an "pemding tasks" field on top of the day/week view.

I like this way of presentation because it clearly shows when, during the day, I have specific things to do and if they do not conflict with my calendar appointments. Standalone tasks apps (like TickTick or Todoist) do not do this. Why do I not want use Google Calendar and Tasks apps? Because Calendar has a problem with notifications (all disappear when the app is opened) and Tasks has a problem with synchronizing and updating recurring tasks overnight. (These problems are not present in the Android versions, only in the iOS versions.)

I do not know much about IT, but read that Google now offers Tasks API which allows an app to connect to their task list. An example of an independent app that does it is Business Calendar for Android. A local task list for those who do not use a Google account would also be useful. I do not know about other providers.

This is a feature I would gladly pay for.

Thank you.