BusinessBeginsHour & BusinessEndsHour - is it possible to have half hours?

It's possible but you need to use another trick: Handle BeforeCellRender event and change e.IsBusiness according to your needs. BeforeCellRender is called for each cell (the cell is specified by e.Start, e.End, and e.ResourceId properties).

You will find a working example in Demo/Calendar/CustomBusinessHours.aspx.cs in the download package.

That workaround works for the highlighting, but is there a way to have the calendar render according to these adjusted business hours when in Resources view? i.e. the visible area is adjusted to show the time between these new business half-hours?

Business hours only work with hour units (i.e. it can't end 17:30).

In DayPilotCalendar and DayPilotSchedulerDynamic, you are able to hide non-business hours (see topic 300). You would still have to use the highlighting for the remaining 30 minute block.