Please go to your Settings and then to Notification Settings. There you can activate/deactivate the options in question by swiping over the button.

In order to deactivate swipe over the button again. Calendar reminders: In order to remove these, please remove them manually from your phone calendar. The removal cannot be steered from our settings.

In order to allow push notifications in general:

1) Make also sure that your iPhone settings allow push notifications. You find this setting under Settings / Notifications and then under Lifesum / Notifications.  

2) See also to it that you are allowing Settings/General/Background App Refresh on your iPhone

Please note: when you use an Apple Watch and your phone the notification will appear on the device that is unlocked.