I think you've answered your own question, but I'll try to clarify.
Q1:
If the person is actually plotting treason (the accused player has
previously initiated such an action with the GM), it adds a -1 to the roll
for an NPC MoS per the rules in the book.
The 'trumped up' means that the CoPS is responsible for developing a
storyline and arresting the person. If this coincides with an actual plot,
even better for the CoPS since the -1 carries across the board.
However, there was no actual guilt/treason in the JSJ/AdS affair since
JSJ had not initiated any treasonous plots with the GM or performed any
treasonous acts.
The real issue then is that the CoPS only had duelling arrests to his
name, and those are "ceremonial" as is the MoJ arrest and any direct King
requests. See question 2.
Q2: "Furthermore, arrests made directly at the behest of the King, or
other ministers (e.g., MoJ for embezzlement), or duelling arrests do *not*
count toward your PC arrest requirement."
You are correct. The CoPS is used in *press* alone for such arrests.
The CoPS does not issue an order for the arrest in the MoJ (it must be in
the MoJ's official orders), direct King, or duelling cases, and so they do
not count toward his 1 successful PC prosecution in the first six months or
toward the 5 arrest limit.
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While we are on the subject, the MoJ will be notified if an embezzling
character fails a roll. Unless notified by the GM of attempted
embezzlement, the MoJ cannot take any action. If notified of a failed
embezzlement, the MoJ can bargain with the accused character or else order
an arrest. NPC MoJs are handled according to the table in the rulebook and
can be influenced.
If the MoJ orders the character to be arrested, the CoPS is the person
used to carry it out in *press* but it doesn't count toward any of the game
mechanics for the CoPS (5 arrest limit, 1 PC arrest requirement, etc.).
The MoJ must arrest the character while he is still holding office.
However, the MoJ arrest is always processed first.
For example,
Jan: AdA embezzles money
Feb: AdA embezzles money and is caught. MoJ is notified
Mar: MoJ orders arrest. AdA resigns appointment.
In this case, AdA is arrested and tried per the rulebook. If the MoJ
had failed to issue the order in March, then AdA would have escaped since
an arrest in April would be too late - AdA had resigned.
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