What was the process for the creation of portraits (like the one of Margarey that Renly shows Net in AGOT) in the middle ages? Would Margary have to sit as a model? Were there court-employed official painters or would the portraits have to be requested with a free-working artist? Given that many european rulers patronised the arts greatly, what was the purpose of commissioning a portrait, or a painting in general? And why do we see so little of them in ASOIAF?

In the absence of photos to reference, yes Margaery would absolutely have to sit for a portrait.
Westeros doesn’t seem to have official court positions for artists; instead, it seems that they’re more court-adjacent specialized labor, similar to the high-end smiths of King’s Landing, who are patronized by the nobility of the court.
There could be many reasons to commission a portrait or painting: as with Margaery, miniatures and portraits were frequently used in the process of arranging marriages (although one did have to be wary of the artist slanting their work for side payments or for personal safety, see Hans Holbein and Anne of Cleves). Larger portraits or paintings could be given as a sign of royal favor, or as gifts for far-flung relatives, or displayed by the monarch themselves as a sign of their magnificence.
As to why we don’t see more portraits, they haven’t really been plot-relevant since Margaery’s in AGOT.

Published by stevenattewell