No.
Yes.
Yes. (Actually, I think there’s a way for quick amputation even outside of hospitals, but let’s not get too technical here. 
I don’t see how A would recuperate in time to mail the arms anywhere before they were so rotten that the stink would be a massive giveaway. I’m not even sure if A would survive the experience. Certainly not without help to bandage the wounds.
Oh.
So how is A supposed to pull this off, while in a hospital with people all around who are going to prevent it? And wouldn’t there have been a huge fuss on the news about the character who went into, or was already in, a hospital and somehow managed to cut both of their arms off – which fuss C would have been watching for, as opposed to the equal fuss about the wino found with both arms cut off (though I suppose A might have concealed the entire body and it hasn’t been found yet by the time C sees A with arms still on.)
– ok, at this point I guess I’m just fighting the presumption. But I’m having a lot of trouble getting past this to think of any way for this story to make sense.
Was there a medically-justifiable reason to amputate A’s arms?
Was there anything wrong with anyone’s arms prior to the intended amputation?
Is there any actual supernatural element in this story?
Does the story depend on anyone (perhaps incorrectly) assuming that there was a supernatural element involved?
I’m having a tough time with a guy cutting off both his arms off by himself and not only surviving but jauntily strolling off to the UPS store. I know that’s not what actually happened (hence the hobo) but that was the expectation.
Is that scenario part of the lateralness of this puzzle?
Is it a “Don’t fight the hypothetical” scenario?
Would a living, arm-having A have presented some sort of threat to C? (Read “threat” in a very broad sense.)
Does any of this have to do with the 2nd Amendment right to bear arms?
This one seems to have died out. Let me know if anyone still wants to give it a go; otherwise, I’ll post the answer my group got and the puzzle poser ages ago agreed we had it.
Died out? There are 4 question posts still waiting for your answers. We’re still playing.
In addition:
When B shot A, had B already received the hobo’s arm?
If not, was there a certain time by which A had to do the self-amputation?
Does any of this have to do with insurance?
In a similar circumstance, would C have shot A?
Were two associates of A needed for this plan? In other words, could just A and B have been in collusion and the story would have played out the same?
Instead of C, could the third person had been random dude D? Like (and I don’t think this is a solution, just illustrating what I mean) A, B, C are all siblings and the fact they’re related is critical. The puzzle wouldn’t work if D was in on it but not a sibling.
No.
I’m assuming you mean the amputation of the wino’s arms. Yes.
No.
No.
What can I say? We were young soldiers, bored, living in the barracks in an expensive place; and most of the new soldiers had an early curfew.
No.
Let’s go with Yes.
No.
No. (Too bad you didn’t write bare arms. )
Yes.
Actually, Yes, there was a deadline for the self-amputation.
No.
Yes.
I had to think on this one overnight. No, if there had just been A and B, it likely would have played out the same.
No, no random dude in the solution.
And thank you, @Saint_Cad for pointing out that there were questions pending! (I’ve been busy. Remember, one of my heros is SNL’s Middle Aged Man (I think he was on SNL).
Had A promised to donate his own arms to C for an arm transplant ?
Had A lost his arms to C in a bet ?
No.
No. (It was not really a bet.)
Did A set to benefit from sending the arms or was it a sort of punishment?
From this, might we assume that A made some sort of, shall we say, “poor decision” in his dealings with C that led to this whole awful arm thing?
At the time this plan was set into motion, was it possible that events could have played out in such a way that A might not end up being expected to cut off his arms?
Did A enter into this plan aware of the risk? (As opposed to the arm-cutting originating at some moment after the plan commenced)?
I don’t know about y’all but I keep thinking of that Scarface shower scene.
Have we made any headway in this at all? I feel like we are at the same spot we were when we started.
Yes, a decision was made in the past which led to the whole arm thing.
No, I don’t think so.
Yes, A entered into the plan with full knowledge.
I’ve never seen Scarface. I’ll try to get to it this weekend.
Yes, y’all have made headway.
Might the person who received the other arm have killed A if he/she had seen an arm-having A first?
Is all we have remaining to solve is determining what sort of arrangement A had with C?
Was cutting off the arm meant as some kind of punishment of A by C?
Was the sending of the arm purely for proof that the amputation of A’s arm had occurred or did C have a use for the arm?
Did C know that the other arm was supposed to be sent?
Did C know where the other arm was supposed to be sent?
If A had sent C his arm but had failed to send his other arm to the other address would C have been satisfied?
Do tattoos come into this? Sorry if already been asked
I still want to know how A was expected to talk the hospital personnel into the original plan. Though I suppose we won’t get that information until we either figure this out or give up.
Yes.
Yes.
I’m going to have say Yes (as a payback).
Yes, the arm sending was for proof of amputation.
Yes.
Yes.
I think if C would have been satisfied so long as C did not see the arm-having A after receiving the wino’s arm.
No.
“Don’t fight the hypothetical!”
On a serious note, I suppose we can say that A decided not to talk the hospital personnel into the plan.