One of the main benefits of building a 2-3 space wide room is that the price of each upgrade drops massively relative to the amount of food, power or water (or other goods) that the room produces. The overall price is higher, but a 3x wide room will cost 500 for the first upgrade, where as 3 single-space rooms will cost 250 caps each for a total of 750 caps charged for the first upgrade.
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Your vault door needs to be upgraded to increase its health. Early on in the game you don’t have to worry about being attacked, but later on you will REALLY have to worry about getting attacked, so you will want your vault door to have the highest health possible, because if it gets smoked, your resources will start getting stolen.
Place the smallest amount of Dwellers in the largest rooms, and the largest amount of rooms, as possible. At its best and most efficient, you should have nothing but 3X rooms with one dweller inside of each one. That will keep them EXTREMELY happy and your resources extremely high, especially as long as your Dwellers’ skills match up to that which is required by said room.
Right now there is no way to get rid of a Dweller that you don’t want, but there are some tricks to get rid of them. The best cheat to get rid of a Dweller is to move everyone else out of the room, and then rush the crap out of the room. Their health will drain as they fight the fire or the Radaroaches, or whatever other plague befalls them. When the health drains to zero, they’ll die off. Don’t revive them. Let them die. Then replace them with new dwellers or just leave the space empty to drop the amount of resources that your vault uses overall.
Get rid of the rocks in order to make more space in the lower regions of the vault for more rooms. After you do that, in order to access the next floor down, you will need to build an elevator right below the existing set of elevators. Once you do that, then the whole next row will open up to you for your use.
Keep your number of rooms to the lowest level possible for the greatest efficiency possible, and for the highest happiness rating for your dwellers. It is almost always better to upgrade rooms as opposed to building more rooms, and generally more rooms should only be built when they can combine with identical rooms, which always leaves you with more options.