a) Does “Party per fess” indicate the shield was divided into three sections horizontally?
No, the word 'party' just means 'divided'.

b) If not, what is the purpose of “Party”
To denote that the field of the shield is parted in some way.

c) If so, how were the sections coloured? Was it gules, vert and gules (top to bottom)?
No, not in this case. They would be Gules Argent and Vert.

d) How does one draw the “fess argent between two plates” (i.e. how does one draw a “fess” on a shield that has itself been defined as “Party per fess”?
Actually it says 'a Fess Argent between two Plates in Chief and a Crescent in Base'. Possibly a less confusing blazon might be "Tierced per Fess Gules Argent Vert in Chief two Plates and in base a Crescent Argent. See image attached.