I wonder if the scratch that Shane got a while ago was the reason he became more animalistic... Ever since then, he had been getting more and more extreme.
But with Randall, I thought he just pistol whipped him in the forest, and left a scent of blood for walkers to get him. Hence him hiding his gun in the shrubs.
And as for Rick still hanging around his dead body, I'm sure he was just having a tough time. He just killed his best friend, I doubt he had the willpower to stab him in the head right after. Or maybe he was waiting to see if what the doctor said was true about everyone being infected. Assuming that's what the doctor really told him.