Can I use different cutoff times on different days, or ship only on certain days? (Essential Estimated Delivery Date app)

Ship only on certain days: yes. In the widget's Conditions tab, select only the days you work in Processing working days (for example, only Monday). Dates then move to the next selected day. Use Order transit days the same way for the days orders are in transit.

Different cutoff times per day: not at the moment. Each widget has one Processing cutoff time that applies to every working day. For example, "4 PM on weekdays, noon on Saturday" can't be set in one widget.

Skip a specific week or date: add it under Blocked dates (Holidays). See How do blocked dates (holidays) work? in this FAQ.

If you need a more detailed schedule, let us know and we'll add your vote to the feature request.