How do you think Maesters get assigned to a house? Does the house just ask the Citadel for a Maester and they sent one, or do you think it’s a more complicated process?

I think the Citadel sends them using its own system, which probably involves factors like what links the maester has (there’s probably a core of necessary abilities like ravenry and medicine at the very least), where the maester came from (note that maesters rarely serve in the kingdom they’re from, to avoid the temptation of bias for their former family), etc.