Ill answer your questions to the best of my knowledge in sequence!

1: No. Weapons dont have a hidden bonus Special damage bonus. However, every weapon does more damage when you have higher strength, with ten strength obviously being the max. The bonus is decent from what I can tell, so you do want to keep that in mind. 10 strength/endurance/luck dwellers are who you want in the wasteland.

2: Endurance = more hitpoints, for fires, radraoches, raiders, exploring, etc. So you take longer to die and waste fewer stims.

Luck = Helps with finding better loot and more caps in the wasteland. In the vault, it increases your chances of getting cap from a room, and high luck also reduces the chances of a room failing a rush. I have some rooms with all ten luck guys, they have a 0% chance to fail on the first try.

Charisma helps makes babies faster, and it also makes your dwellers better in the radio station. Aside from that, charisma is kinda a worthless stat.

The other skills only effect their production rooms efficiency. I have heard rumors that they might effect your wasteland drops, but not in a statistically noteworthy way.

3: Yes. The strength of any random outbreak/raiders seems to use some kind of average level algorithm. So having one level 50 guy in a room with 5 level 1 guys is going to doom the level ones to death. Likewise, having a room of only level ones makes the playing field rather even. They stop getting better once the entire room is level 50. Just make sure you continuously are pumping out a good number of stims every 5 minutes or so. I have a level 3 medbay thats a triple sized room. It makes me 12 stims every 5ish minutes.

4: I previously mentioned it, but having maxed attributes in the Special relevant to the room + max luck leaves you with a near 0% chance of failure.

5: I cant make heads or tails of this question, but I think the answer is this; Failing a rush loses 10% happiness. Succeeding a rush gives you 10% happiness. The amounts lost or gained are not related to the chance of failure, they are constantly -/+10%. If you are multi rushing a room, that your choice, but it gives no bonuses besides the stated caps and XP.

6: Most definitely. I essentially have a factory going on. First thing a new dweller gets is maxed special stat in the room they ill be working in. Then they get a minimum of 5 endurance, then a minimum of 6 luck. This make it so they can take decent of punishment, have good odds for rushing, and are productive as hell. For any dwellers I already have that fail to meet any of these requirements, I'm slowly going back and training them up when there's an available space in any of the training rooms that they need.

There's nothing wrong with taking in low level explorers though. I just immediately drop them in a training room for a day or two.

just be careful, as this method leaves you with a LOT of dwellers that arent being productive in any manner, because theyre training. Always make sure you have the food/water income to spare when inviting a new person into the vault. Otherwise they can wait topside until you're ready!