Fallout Shelter- no attacks ever

Ok, I will address the issues as I come across them:

• It is indeed cheaper to build one large room and upgrade it all at once than individual parts (upgrade discount is 25 % for size 2 rooms, 33% for size 3 rooms). If you have the option to build in this manner then always do so.. Running low on some resources though can make getting a single room more important.
  • NOTE: The exception to this, from my knowledge right now, are the radio rooms. A larger room will reduce the time a bit but not increase the chance at the end of that time of getting a new dweller. It is better to have single individual rooms for this (though I will admit I have not answered the door in over a month myself). Radio Room bonus happiness is based only on the number of dwellers assigned to it (observation with a size 3 Radio Room, putting 6 dwellers with 1 charisma or 6 dwellers with 10+ charisma yeld the same 6% happiness boost).
• Room production is very simple and straight forward. Each room produces a resource of a certain amount. That amount is directly tied to the size and upgrade level of the room. The time it takes for the resource to be made ready for collection is also an initial fixed time based on the same factors. Your workers then combine their appropriate stat together and reduce the time it takes for the resource to be produced. Dweller stats have diminishing returns on production cycle duration (having a dweller with 6 PER in a water room won't give half cycle duration as assigning a 3 Per dweller).
  • Basically this means that one worker with a stat of six is equal to six workers with a stat of 1.
  • Luck adds towards this score for any room and also assists with the random caps bonus you can get. I am not sure what the chance is to get caps but by going over the cap of the primary stat with luck, you can reduce the time and rush failure rate significantly. I so far have gotten one rush to 0% followed by a 6% chance of failure. I have heard reports that you can get 0% twice in a row with enough points. Having all your dwellers with 10 Luck and 10 in the romm-related skill yeld 0 % failure on first rush, increasing with each rush.
• For the raiders, the room does not matter. Health is determined by the people's levels. Their damage is determined by the weapons you give them. You basically want the first room with someone in it to have the best weapons inside your vault. Endurance -may- have some impact on damage taken but not enough to make it noticeable as compared to level variance of the dwellers (endurance is directly tied to HP gained when they level up : a dweller with END5 will gain less HP when leveling than an END6 dweller, confirmed by reading values in save file [all dwellers have 105 base HP at lvl 1]).
  • My first room was my diner and now garden.. My staff are just armed to the teeth with the best weapons.. 2 of the 3 raiders drop dead before they even make it to the middle of the room.
  • Do NOT use the gate room for defense. You can only put two people in there.. its just not as effective as a full sized room can be.
• Layout of the vault has nothing to do with the attacks. The only thing to be concerned here is if something happens in an empty room, usually rad roaches but some times fire, that they will spread until a room with people in them are found. After that they will only spread if they kill all of the people in them.
  • Simple rule of thumb, arm everyone in your vault with guns. The best ones should be in your diner to stop raiders since they steal resources vs the other events just annoy the room they occur in. But cycle the weapons from First Room to Wanderers to Everyone else until everyone is armed. As you get better weapons, spread them around and upgrade people.

And so much for a short answer.. If anything needs more detail let me know in the comments.

Edit: Redid the Luck section based on @SkyHiRider's information in the comments.

The radio room does two things: raise happiness for other dwellers and occasionally attract outsiders to join the line outside your vault.

I have not tested the happiness mechanics in any depth, but that functionality is described on a loading screen so I assume it works in game.

Attracting outsiders works a bit differently from all the other resource production rooms. The standard resource rooms run for a set time, then flash with an icon when the timer is done and you (or Mr. Handy) can tap the room to collect the resources. Merging the same room into a bigger room increases the time it takes to generate the resources, but also increases the total amount of resources collected at the end. Staffing the room with dwellers high in the room's stat decreases the time for the resource cycle to complete.

The radio room is different. Each time it completes its cycle, it has a chance to attact a single new dweller. If it fails that chance, it immediately starts a new cycle, whether you have the vault open or not. It repeats this cycle until it successfully attacts a dweller. When that happens, it pops the icon and waits for you to tap it. Merging radio rooms together and upgrading the room both increase the chance of a new dweller at the end of the cycle as well as increase the time each cycle takes. Staffing the room with high charisma dwellers decreases the time taken per cycle, but does not affect the percentage chance per cycle.

What this boils down to is that a fully upgraded, full size radio room with six dwellers of 10 charisma each should attract a new dweller faster than a small radio room with a single low charisma dweller, both because each cycle is faster and because each cycle has a higher chance of attracting an outsider.

As a point of reference, my vault with a top of the line radio room with 6 dwellers of 14 charisma each (10 stat + 4 cha outfit) consistently attracts a new dweller every 6-8 hours or so. I send the outsider to die in the wasteland if their stats are not what I'm looking for, but that's a different thing. It's also rumored that assigning Three Dog to the radio room does something special, but I haven't confirmed that.

I also have not tested multiple radio rooms in the same vault.

tl;dr:

Yeah, it's that slow.