Following expression can be leveraged to find the difference between date fields {% let currentDate = now %} {% let currentDayOfYear = dayOfYear(currentDate) %} {%#if currentDayOfYear - dayOfYear(<another date field>) = 4 %} element_1 {%else%} default_element {%/if%} 

In the past, I have seen this error surface when the push credentials could not be retrieved from the app surface for the respective appId at the time of sending due to a maintenance on launch/data collection

This won't be feasible using journeys. You can explore Data access API https://experienceleague.adobe.com/docs/experience-platform/data-access/api.html?lang=en and it will be a pull from the downstream system instead of a push from AEP/AJO.

No, you won't be able to use it for personalization at the moment.

You can leverage tags and this would be available in the ajo entity system dataset

Event data can be accessed only if the journey starts with a unitary event. 

Accessing events via yyy.profile.timeSeriesEvents.zzz will not work. You can create a batch segment leveraging the attributes (feedbackstatus, eventtype, timestamp, journeyversionid) of message feedback event dataset and then exclude this segment in the condition node using inSegment() function

Just trying to understand the need for an explicit count check as the previous condition will only let those profiles which you are filtering. If you want to visualize this in a report to understand the number of profiles passing through either of the transitions, you can enable the "Show path for o...

You can refer to the below note in documentation https://experienceleague.adobe.com/docs/experience-platform/xdm/tutorials/relationship-ui.html?lang=en where it is not recommended to have relationship's between schemas of same class 

Not at the moment, Currently supported functions are documented here https://experienceleague.adobe.com/docs/journey-optimizer/using/content-management/personalization/functions/functions.html?lang=en