You didn’t answer the question you just threw out a derail.
People saw him shoot the cop in the head in the middle of the street and they kicked his ass. He was bruised up.
why did Oswald not have his pistol on him when we was at the Book Suppository? why did he need to go home to retrieve the gun and then shoots Tippet and then goes to the theater?
my opinion is they had Oswald "motivated" to shoot the president, maybe he was there to do so, they gave him a garbage rifle with barely attached scope in an OBVIOUS "nest". when the shots started going off, Oswald knew he was setup at that point, because he didnt actually pull any triggers. The kill shot came from the rail yard side from a mercury tipped 221 fireball.
after that, Oswald knew he was the patsy and had no idea what to do. so he had to go home to get his revolver and then from there its just a chaotic scene of a guy who never really thought it through. Maybe he thought his CIA/Mafia handlers would get him and usher him away from the building? who knows. thats the whole reason Ruby shot him.