Think I've found a possible solution to both questions, after reading to the bottom of this thread
By using the ScrollTimeRuler
method of radScheduleView, I can scroll the horizontal scrollbar to the current time of day, minus eg. 6 hours to see a little of the "history" as well. Just need to do this periodically, and the positioning should be fine then.
I guess I also need to ensure that there is always eg. 3 days of future appointments in the view, maybe by reloading the dataset every hour or so.