Not entirely true Johan.
Yes, Princess Amalia could ask her mother to become Regent for the time being if called onto the throne now, but she can't make that decision on herself.
The government would need to send a bill to that effect to the parliament and the parliament would have to vote on it, allowing Queen Maxima to be a regent for her daughter for a fixed period of time (f.e. until the 25th birthday of The Queen (Amalia)).
It is not something Princess Amalia and her mother can decide for themselves.
A regency can either be declared if the monarch is incapacitated and needs someone to step in or in the worst case if the monarch dies and the successor is still under age. The Princess of Orange who just turned 18 last month seems to have indicated that a third option would be possible: if she had to succeed while she is still studying she would ask her mother to act as regent in case the King was to die.
Basically the heir or heiress to the crown once adult it generally the first person to be called upon if the monarch needs a regent. If the monarch is a minor than it can be either the remaining parent who steps in as regent or a/the first grown up in line of succession.
Both have happend. Until Amalia turned 18 her mother was the first to be regent if the princess were to succeed upon the death of her father will still being under age. Uncle Constantijn was named as a second option in case something were to happen not just to the King but also to Queen Maxima.
A similar arrangement was in place between 1980 and 1985 during the minority of the current monarch. His father prince Claus would have become regent with aunt princess Margriet as a replacement.
In Norway, Sweden, the UK, Denmark, Belgium, Luxembourg and Liechtenstein the successors to the currently reigning monarchs are all grown ups. Only in Spain and Monaco is the first in line of succession still too young to succeed and take on the role themselves.
I believe in Spain Queen Letizia would be regent but i might be wrong and i suspect that Princess Caroline seems te most likely option as regent in Monaco in case something were to happen to the sovereign prince before prince Jacques turns 18.
In the Netherlands the Princess of Orange is the person who would become regent in case the King was unable to attend to his duties for more than a few weeks however if she were to succeed by the death of her father she could ask her mother to step in as regent for a few years to give her time to prepare. Let's hope neither scenario will ever be needed.
Generally, what are the circumstances for declaring a regency?
Underage of the next sovereign (D.Pedro V, Wilhelmina, Alfonso XIII), health problems, physicall (IIRC there was a blind duke of Brunswick and I am not speaking of George V of Hannover) or mental (George III, Maria I, Ludwig II), political reasons (Pr.Charles of Belgium after Leopold III's abdication)
Prior to her husband's death did Queen Elizabeth have plans in place for such an event?
Yes, she did.
Do other monarchs, please?
If they have minor children, they usually do.