Yeah, building a new city after medieval is a suicide. Ammount of buildings to scroll through to find the one you want is insane.
Also, sometimes when traded an event tech, AI gets the even of getting 1 archer or the galley or the trade caravan even though I already got it. AI trading these techs also seems to trigger the event - even though the trading party didn't have it.
As for inquisitor training AI seems to handle this well exept for situations when his state religion is changed because of espionage or diplomacy. He then trains inquisitors to purge his previous state religion (sometimes even the holy city he has) and starts to spread the new religion, after a while he converts back, purges the religion he was forced to convert to even if he doesn't have a holy city any more (because he purged it himself) and stays on intolerant civic for extended periods of time even if it is not needed anymore if he has at least 1 inquisitor (at least that's what I noticed).
For ex: AI has 1 city with non-state religon left. He trains 3 inquisitors, goes to purge the religion, after it is purged the remaining 2 inquisitors stay in the city and he doesn't convert back to any other religion civic. If I however spread the religion to other cities and he manages to purge them all and not have any inquisitors left he changes his civic to free church or state church. Including a script to remove inquisitors during anarchy or after the change (for ex: people lynching them) would probably solve this issue.
Also: after monastery is obsolated the player is able to train missionaries from all religions present in the city, not connected to the monastery itself (ex: having an obsolated confucian monastery in a city enables the player to train Priests if Christianity is present in a city) - don't know if it is intended.