I don't think there'd be any appreciable damage to the barrel itself.  I know that the good old M-16/M-4 barrels are a pretty high end alloy containing things vanadium and molybdenum and suchlike.  Now, if the slug hit the actual mechanism you could cause all sorts of malfunction.  Well, probably nothing spectacular, just make it seize up and call it a day.

Yep.  Paynesgrey is another Forum denizen whose gun-fu is strong, if you need practical info on things that go BANG!   

As a flip-side, what would you consider the most generic, everyman sort of name?  In other words, the last name you'd expect for a hero/villain to have?  My current short list is Larry, Bob, Jim, Bill, or maybe Murray.

Any diminutive, like Billy, Bobby, Artie, Frankie.

Shot, even buckshot, wouldn't have much effect on a gun barrel. A 1-ounce soft lead 12ga. slug moving at 1500 feet-per-second might deflect one barrel, if it hit it just right, but that would only affect the accuracy of one round out of six per revolution.  The most effective way to take a minigun out of action with a shotgun would be to shoot its operator.  If the plot requires destroying the gun itself, you'd need something bigger, like a .50 Browning machine gun or sniper rifle that could smash the mechanism, or a rocket propelled grenade.

I always wondered if Glen Cook's Garrett PI was given that name as a nod of the head to Randall Garrett. Before the Urban Fantasy trend Lord D'Arcy and Garrett PI were the best known (at least to me) investigators in worlds where magic is prevalent.

Yep, Randall Garrett and Michael Kurland, and other Sci-Fi, Fantasy and Detective writers who knew and liked each others' works would work the other authors' names and characters into the stories. In one of David Weber's Honor Harrington sci-fi stories, in the far distant future, one of the characters is reading an ancient Earth detective story featuring "Garrett Randall, P.I.".

Hmm, thought there was three or four...maybe I made them up in my mind. 

That is a universe I would love to be able to write in. I wonder if there is any fan fic anywhere online.

Pretty sure there's probably a ton of fanfic out there, but I haven't gone looking for it.   
Michael Kurland collaborated with Randall Garrett on some of the short stories, and he pops up as a character once or twice. The two novels he put out were authorized by Randall Garrett's estate.

I loved the Lord D'Arcy series. I was unaware that anyone had continued them. I will have to look for the Michael Kurland stories.

Michael Kurland is pretty good, and blends seamlessly into Randall Garrett's universe with the novels A Study In Sorcery and Ten Little Wizards.  Kurland also has another series all his own, featuring Sherlock Holmes' nemesis, Professor Moriarty, as the protagonist.

When NASA sent the Voyager probes on a trip outside our solar system, they put data about Earth and our solar system embossed on thin gold plates attached to the spacecraft.  A scroll of gold, or gold-plated alloy could hold a considerable amount of data, and be rolled up compactly inside  a heavy protective armored tube to suvive a considerable amount of impact force.
Getting many tons of cargo from an Earthlike gravity well to a nearby moon with 1940s technology is doable, if not exactly cheap.  An enlarged V2 type rocket with an extra stage, all the way up to something like an Atlas booster like the ones that sent the Apollo missions to the moon would be feasible, using hydrogen or some hydrocarbon fuel with liquid oxygen.
Launching thousands of cargo rockets is no problem in a controlled economy.  There were even plans in the late 1940s and early 1950s for using an atomic power plant to power a plasma rocket engine, but those got scrubbed because of civilian concerns about radiation damage if one ever crashed. Those concerns would be unlikely to stop a project under a totalitarian government, it would just relocate the rocket base away from population centers near the capitol.

Has anyone done anything with intelligent zombies that only eat brains of livestock?

In the Xanth fantasy series by Piers Anthony, there is at least one zombie love story. In Xanth, when a zombie falls in love, it becomes more and more lifelike, until it practically regenerates, as I remember it.