If you are still looking for the Asana alternative, try Quire. It has all the features you need. It's pretty simple and powerful.
I use Google Calendars. You can sync on pretty much any device. On Mac, you can just sync it to the Apple Calendar program. They have an Android app here:
https://play.google.com/store/apps/details?id=com.google.android.calendar&hl=en
To have it send you an email summary, log into Google Calendars in a browser, to go to the Gear icon > Settings > Calendar (small blue link, upper left) > Edit notifications (for the calendar you want). Check the box for "Daily agenda" and click the Save button. As far as Facebook sync goes, it looks like you can add birthdays & stuff by copying the URL:
https://androidscrib.com/how-to-sync-facebook-events-to-google-calendar/