1) The game puts no cap as I know of on any of the spaces where you draw Denizen cards, that's why we capped it to 3 but still allowed to replace the oldest card with a newly drawn one. Denizens that have been visited only stay if their TRAIT description matches the space they're in, or if it states "any". So you can see these corner spaces, plus others, can build up Denizens rather quickly where a player will take a long time deciding who to visit out of several Denizens.
2) Yes cards were shuffled, even if they weren't it wouldn't matter since Denizen cards are drawn on random spaces visited. (i.e. the top five cards have City as the Trait but each time they were drawn it was on the Graveyard space, Village, Tavern, etc.)
3) The problem is reading multiple Denizen cards in a single turn trying to decide who to visit, therefore eating away playing time. And since we were playing a house rule where the Denizens fluctuate as the oldest card gets replaced by a newer one, the space then always becomes unfamiliar. Unlike the original board, as Joker has stated, memorization of a space becomes difficult when playing by the house rule I had. Original rules, all matching trait Denizens would stay + un-visited Denizens, so instead of reading 3 in my house rules you'll read cards that you're familiar with since the beginning of the game plus the ones stacking all the time later with no limit.
4) Denizens makes the spaces different every time you play with this expansion. The con is the unfamiliarity will eat away time, because we have a hard enough time as it is already to reach the Crown of Command with just 4 players on a 4 hour time limit. (We're adults, we work and/or have families/responsibilities)
Most of the cards are those roll a die as you've mentioned, but there are some that can really screw you over such as the Black Knight: "Pay one gold to take a life off of any player of your choosing." That's how I was killed. Swear, if you're rich and have a poltergeist, you are set.