The barber paradox shows that an apparently plausible scenario is logically impossible. It was used by Bertrand Russell to illustrate his Russell's paradox (that set theory as it was used by Georg Cantor and Gottlob Frege contained contradictions).
The barber paradox posits that in a village, the barber shaves everyone who does not shave himself, but no one else. The question that prompts the paradox is, who shaves the barber? The barber can neither shave himself nor not shave himself. The question "Who shaves the barber?" is unanswerable.
When Lorne (Billy Bob Thornton) is questioning his employer, the telephone-choice "Hearse or ambulance" is a reference to Sling Blade (1996), in which Thornton's character is in a similar dilemma.
The human body is, in some ways, very resilient. You can live with part of your lungs gone, with half of a liver, with one kidney (or no kidneys if you can get renal dialysis). Losing your entire spleen mostly just makes you more susceptible to bacterial infections. The big danger with a ruptured or shot spleen is how fast you can bleed out without immediate emergency surgery.