I have a different idea. I thought the Inner Sanctum was the most difficult basic scenario for Keeper, when I first read the whole Keeper's Guide.
In the real game, my Investigators chose awfully bad Character-Item set - the ONLY starting weapon was the Guitar. However, it was really hard for me to win. They found shotgun, they stunned several cultists with fists, I was always lack of threats, blahblahblah. I never thought Joe Diamond with Cult Robe and Magnifying Glass could be that powerful. I won the game because the two Shoggy made several miracles (especially slamming the Barrier with one shot)
I thought it was because,
The keeper should move ALL THE CULTISTS with Command Minion, requiring 1 threat for each cultist. Thus, the Keeper cannot save any threat while moving 4 cultist each turn, even with 4 investigators. There is no free mythos/trauma with Evil Presence. The ONLY other threat source is Event 2, and there are no Take Sample, no Blood Relative, etc.
It is a extremely long trip between the Altar and the Chapel. The only help is the ladder, but the Doggy and the Shoggy cannot use the ladder. Moreover, there is no vent for Doggy.
Cultists are too weak against weapons, especially ranged weapons. Each cultist kill makes the Keeper to spend threats again. The worst one was Tommy Gun - It often TERMINATES 2 cultists each turn. (In fact, it even kills Shoggy in a turn, with the rare case)
I wonder how the other Keepers could play Inner Sanctum that easily.
I think that you nail is pretty much in topic 1 - Which this scenario has been won by Keeper alot - when I hear that people can keep throwing their Cultists at investigators I am puzzled because of the Threat limitation (In case of Inner Sanctum it is 4 x 16 + X being the number of Cultists in play, which at least means up to 16 Cultists with ability to move a total 96, an estimate of 6 each) There is on top of my memory (I didn't check this, please do correct me) 7-8 spaces from the nearest altar to the Chapel. So if a keeper wants to be cheap, and by god does it seem to happen often, a maximixed force can be moved in like that.
I also remind people playing (Another mistake alot of people make) is that a Cult Leader, does not count towards the 4 cultists that have to make it to the Chapel, I refer here to the rulebook, page 12: "Special Note: Cult leader monsters are not considered to be cultists for the purposes of card effects and abilities."
To answer number 3, yes Cultists die easily, protect them as your children, while luck has alot to do with dice rolls, try to play the game story based. When the players do finally get to the chasm the distance between the altar and the chapel is much much easier. Allowing for a quick summoning of the Cthonian, with the chapel being not much further than 3-4 spaces away (The cultists were apparently in such a hurry they forgot about that ladder before the Investigators found it, supposedly it was a cultist that couldn't find the ladder that called them?). Look at the map as a keeper and think about baits, possibilities and movements, there is no shame is sitting with a scenario beforehand and overview your possibilities. And if all else fails, put a Shoggoth in a room that you don't want the players to enter. Or bait them to that room. Play with their expectations, or their paranoia of your hidden games.
I would recommend sitting a Shoggoth down in the first Altar room, and just… sit there. It doesn't have to do much else to protect the Crypt where the last Clue is (Yes, it is relatively easy to dodge with a modifier of +0, but it's damage is massive). Wait for the investigators to either waste time killing it, moving cultists out of the room, but keeping the Shoggoth there, alternatively leave a few cultists behind to cause either evasion checks or turn them into hounds if near death. Or make a Shoggoth move to a room that is important, one of my first moves in one game was to make a hound, and then move it to the bathroom, paralyzing the northern end of the map. While I have yet to win this scenario, I have been close, had it not been for an extremely lucky karate chop delivered by Harvey, that killed himself as well, and I couldn't ask for more heroic and fun ending ever when I was like "Mwahahaha I will win" until Harvey (Now with-out spell because he failed), moved into my space, did a flipping 1 roll on attack and made the Cthonian explode in a bile of goo.