Partial Paralysis: If the piece X is attacked by the piece Y then X cannot move as Y.
Leffie: A move is illegal if it leaves a piece paralysed in Eiffel. (introduced in Quartz 46)
Eiffel Chess: Units, other than Kings, are paralysed when they attack each other. The paralysis occurs in the sequence P-N-B-R-Q-P. A Pawn paralyses an enemy Knight; a Knight paralyses an enemy Bishop, and so on. A paralyzed unit loses all powers except that of causing paralysis. Fairy pieces play normal, without paralysis.
Neutral piece: Belongs to whichever side chooses to use it. It can therefore be moved or captured by White or Black, and in Circe it is reborn according to capture. A King may not be moved onto a square controlled by a neutral piece, because of self-check.
Explanations about the mates:
(I) Black cannot move the nQ away from the bK due to:
- Leffie illegal moves: 4.nQa8?? illegal because of nRf8, 4.nQa7/nQa2 illegal because of nPf7
- Partial Paralysis: 4.nQa6/nQa4/nQb6?? are impossible because nQ partially paralysed by wK
(II) Black cannot move the nB away due to:
- Partial Paralysis: 4.nBxg7? impossible because nBf8 partially paralysed by nPg7
- Leffie illegal moves: 4.nBc5?? would be fine from the point of view of Partial Paralysis - nB partially paralysed by bK – but it is illegal according to Leffie due to the presence of nRb6. Of course 4.nRd6?? is also illegal due to Leffie
Comments:
Promotions, specific mates, “mysterious” moves by promoted nR (3.nRf8 and 2…nRb6)
In (I) c7 gives mate, g8 promotes with Leffie motives, f7 blocks
In (II) c7 promotes with Leffie motives, f7 gives mate, g7 blocks. (Author)
That’s right, Partial Paralysis effectively restricts the nQ’s mobility.
If you enjoy this combination of fairy conditions and the headache that ensues, you can also have a look at G206, SuperProblem 2019. It shows mates in the middle of the board with a neutral Queen and again only 5 units. http://superproblem.ru/htm/tourneys/annual-it/2019/fairies_2019.html
No.1469 
The combined conditions are a little to grasp. In the second solution, I cannot understand why black cannot play 4.nBxg7 defeating the mate.
* difficult to grasp.
As written in the explanations, in the second solution 4.nBxg7? is impossible because nBf8 is partially paralysed by nPg7.
sorry. you are right if course!
In the mating position of (a) it’s important to notice that nQb4 is impossible due to nRf8 (explaining why this rook must go to f8).
Hm, nonsense of course. nQb4 is impossible because of Partial paralysis.
That’s right, Partial Paralysis effectively restricts the nQ’s mobility.
If you enjoy this combination of fairy conditions and the headache that ensues, you can also have a look at G206, SuperProblem 2019. It shows mates in the middle of the board with a neutral Queen and again only 5 units.
http://superproblem.ru/htm/tourneys/annual-it/2019/fairies_2019.html