The single easiest way to get rid of Radaroaches and Raiders is to do the following. Make sure first that all of your good weapons are unequipped. Then, when the infestation comes, go to the infested room and equip the Dwellers with the good weapons. Let them absolutely crush the infestation. Then when the infestation is gone, unequip the weapons and put them all back into your inventory until the next Raider or Radaroach attack.
Fires are a whole hell of a lot easier to overcome, though. For those, all you have to do is get everyone out of the room and let the fire burn itself out. The fire will go out whether you have dwellers in the room fighting it or not, so there is no point in keeping the dwellers in the room. So when a living quarter randomly catches on fire, leave it alone.
Making a baby is fairly easy to do. All that you have to do is stick a male dweller and a female dweller in the same room and leave them alone. They will go into the private room of the dwelling and a bunch of happy faces will appear (you can figure what they are doing). They will “dance”. While they are waiting for the baby to show up, no new dwellers will appear. Dwellers will start to appear again after the baby shows up.
Once the baby grows up, it will have its own SPECIAL stats, so look at its numbers to see what it has going on. You might end up getting a rare dweller or a dweller with otherwise excellent statistics. Try breeding a rare dweller and a common dweller or two rare dwellers to see what happens when their baby grows up!
Getting 100% happiness is very difficult to do, but it can be a whole lot simpler than most people expect. The main key is to keep your power, food and water in the greens and well over the minimums. The higher, the better. Build radio rooms to give your dwellers entertainment and they will be happier. Put men and women together in the dwellings and let them have babies and they will be extremely happy. Keep them from getting sick and irradiated and they will stay happy; if they get sick, damaged or irradiated then they will have low happiness.
Specific rooms can increase the stats of your dwellers. Build an Athletics room for agility, and a weight room for strength. A lounge increases charisma and a classroom increases intelligence. You can unlock these and all of the other available rooms by adding more Dwellers to your vault. The highest room that you can unlock is the Nuka-Cola bottler, which is unlocked at 100 Dwellers.