IIRC, the shoot-out at Lot #42 and on Fremont street behind the OK Corral happened in late 1881.
You're correct that the final straw for the outlaw Cowboy faction was No Carry Within Town Limits. They were fed up with the town leaning towards the Earps' attempts to make it civilized.
If the Cowboys hadn't been so antagonistic since the Earps arrived in their town, Virgil Earp (town Marshal) might have played a different card that day. But the Cowboys had repeatedly threatened the Earps and the Earps lost patience and such is history.
The Vendetta Ride is especially noteworthy and never depicted until the movies Tombstone and Wyatt Earp (Kevin Costner).
For the (2) definitive books on the Earp/Cowboys saga, and I've read many:
1. Inventing Wyatt Earp by Allen Barra;
2. Wyatt Earp: The Life Behind The Legend by Casey Tefertiller.
Both include historical documents, including court records, depositions by eye witness accounts of the gunfight, witnessed commentary by the 2 opposing newpapers (one pro Earp - the other pro Clanton), diary entries, etc. They are difficult reads since they don't follow the timeline well, but provide all the known facts and hearsay and opinions and refute the ancestors of Clantons' assertions by commonsense. They actually claim one or more Earps held up a stage. Nonsense.
Bottom line: The Cowboys were the first known organized gangsters in the West. The Earps were LEO's, although Wyatt was not rehired in Dodge City or Wichita for over-zealous enforcement (pisto-whipping with his Colt). Can't recall, but I think even Warren Earp was a LEO for a short time.
Yes all correct. Apparently gun control started as the civil war ended. Jim Crowe etc to disarm Africans in america.