What happens if you use multiple Major/Minor Scrolls of Insight in a single day? Do the effects overlap, are the later-used ones pushed to the next day, or do they fail altogether?

Blessings aren't cumulative. If both of the used scrolls have the same type (for example, both of them are Minor), the time of the effect will be restored to 24 hours. If you use 2 scrolls of the different type (Major and Minor), the pet will benefit the effect of the Major Scroll.