Are you asking how to do the question?
Basically. I like to decipher a question. Pick up on the major words and look at the diagram really closely!
To be honest, you only really need to decipher the diagram to understand it.
The answer becomes clear if you consider the words neuron, pathway, circuits and the plus signs.
Keep that in mind.
Basically, if the first neuron is stimulated, it will stimulate the other 4 neurons until it loops back. If the first neuron stops stimulating, then the whole cycle stops.
If you can figure that out then your answer is positive feedback. So the initial impulse will stimulate the remaining 4 neurons which stimulates the original message (amplifying it) and the process is restarted again. Continual.
for ii. Why are such networks important to rhythmic breathing?
It enables continual stimulation for continual breathing.
On a side note: if one of the neurons was a minus sign, the + and - would cancel out and no stimulation would occur, which would result in breathing problems etc.
So these circuits allow for continual stuff until stimulation is removed.
Hopefully that helped a bit, makes a lot more sense in my head haha.