Unless part of the game takes place in the outside world, a generic "bad" should suffice. Maybe it's utterly terrible, and the only reason that the whole population of the earth hasn't poured in is that the apartment building is hard to find. Maybe it doesn't matter, because the players can't leave - what used to be the door to outside now just leads to more apartment. Maybe the players don't know, as months or years have passed since they entered. Maybe it varies, because there's more then one "outside" as the apartment bridges dimensions.
1. How much player mortality do you want to see? Is this going to be one of those "bring a stack of character sheets" games, or will players carry the same character through an ongoing long-lasting campaign?2. How dangerous should it be?
2. How much danger can your characters survive? Are they going to be the equivalent of high-level 3e DnD characters, with a ton of hitpoints and a grab-bag of broken abilities - or are they squishy, like 1st-level wizards? Do you characters need safe zones to rest and recharge, or can they sustain themselves indefinitely under threat by e.g. sleeping in shifts?
Once you've answered those questions, the answer you are looking for should be pretty easy to find.
Super-crazy on the creepy/dangerous/disturbing scale, medium to low crazy on the incongruous/wacky/rando scale, and low crazy on the broken/monostrategy/powerful scale.3. How crazy should the stuff inside be?
I recommend looking at the SCP wiki for inspiration.
Why not both? Uncertainty is a key element of a good horror game. Not knowing how sentient a given monster is means that they don't know what that monsters capabilities are, which makes it all the more frightening. It also gives players another thing about the monsters to figure out, which is a challenge that many players enjoy. It also gives the game more variety. There's a lot of reasons to have a variety of levels of sentience, and no reason that I can see to focus on just one.4. How sentient should I make the inhabitants?
Eh, maybe - but stable time loops are a very easy thing for players to break, intentionally or unintentionally, and then you've got a paradox on your hands.5. Should there be timey wimey wibbly wobbly?
That's something that you could design around. Say, for example, you could establish that time loops happen and that Very Bad Things happen if they are broken so that players need to work to maintain the integrity of time loops that the notice. However, if you choose to include the possibility of time loops in your game, this will likely turn out to be something that you need to design around.