Google Tasks sync is performed by aCalendar itself. Authentication is provided through your Google account in Android, thus aCalendar does not ask you for your password, but will ask for permission to manage tasks.
Timed tasks and recurring tasks (offered by aCalendar since many years) are not yet available in Google's programming interface (API), so we cannot work on comaptibility yet.
Google Keep and Google Reminder cannot be synchronized to aCalendar, because Google offers no public interfaces.