Morning,
I seem to be having a problem with my survey123 inbox not working correctly. Iv made tons of these surveys using the same xlsx sheet but the past 3 recent surveys seem to not have the inbox working in different ways. I will attach my sheet its very large but here are some of the problems occuring.
My survey123 is updated to the most current version.
Re. your first point, I just logged a bug for it a few days ago. It broke with the latest AGOL update.
Defect number: BUG-000169089
Synopsis: The ArcGIS Survey123 field app does not automatically recalculate values for date questions with relevant expressions when the record is edited in the Inbox folder.
Status: In Review
Not sure about your second or third point, though I encountered your first issue with trying to calculate the date fields from an inbox survey yesterday.
To get around this, I found the date fields can be specified as a text question type within the survey itself. The calculation will run normally and will populate with your date, but will display it in a decimal format. You then need to set the bind::esri:fieldType field to esriFieldTypeDate which will convert the string of numbers back in to its respective date format in your data frame.
Weirdly, I found this function of calculating dates did not break when the calculation was run within a repeat. Possibly this could be another solution for this issue in the meantime?
Hope this helps! Sorry if I've misinterpreted your question!