Harry Potter and the Order of the Phoenix: Chapter 2

As we are winding down for bed each night, we read a little bit with our toddler. Currently we are making our way through the Harry Potter series and just finished book 4 / started book 5. Book 5 / Harry Potter and the Order of the Phoenix is where my my online Harry Potter book club began which means I have had the chance to engage in thoughtful discussion with other Potterheads about it.

As my family progresses through this and subsequent Harry Potter books, I will post some thoughts from my book club discussions here, starting with the chapter we just finished at home: Chapter 2. Caution: there be SPOILERS below:

• It has always fascinated me how/why Mafalda Hopkirk sends Harry a letter so promptly after he casts his patronus. Is she the only person who would send such letters? In which case, is she on duty 24/7/365 to do so? Or was she just the person on call / on shift at the time? As well as magic works, this should actually be a very automated task, but the fact that Harry receives another letter from her shortly thereafter in response to Dumbledore's arguments seems to contradict that possibility. 
• Or, if the dementor attack was a concerted attempt by the Ministry to silence Harry, was there an entire team of ministry officials coordinating it, including Hopkirk standing by to send the letter as a Plan B in case Harry successfully warded off the dementors instead of having his soul sucked out by them? 
• We actually DO get an answer to this question in Chapter 32 of OotP: 

“He never knew I ordered dementors after Potter last summer, but he was delighted to be given the chance to expel him, all the same...” - Dolores J. Umbridge

• It sounds like Umbridge was operating on her own, not coordinating a Ministry-wide conspiracy to murder Harry, in which case I am still left with my original questions about the inner workings of the Improper Use of Magic Office.