I can receive but not send any iOS Invitation (Shared Albums / Reminders / Calendar events etc)
You need at least one account added on your device to be able to invite. You can add it on Settings &gt; Accounts &gt; Add Account.
If you have a provider specific app you may be able to use it to invite other users to calendar events without the previous step.
Shared albums should not need an account though, just the email or phone address associated to the Apple ID of your invitee, depending on the way you chose to send the invitation.