James,part of what confuses people a bit about chunk shooting is that each chunk shoot is its own event and can vary as the people putting it on see fit. There is (thank goodness) no National Chunk Shooting Association making standardized rules that everyone has to follow. Like the ramrod question, some shoots don't care, others require that a ramrod could be held under the barrel. The chunk shoot in Iowa near Ames allows underhammers, but the hammer must be powered by a spring that serves as the triggerguard; that is their rule.
As to the circles on paper targets, they are to make scoring easier; any shot outside the circle is given an automatic number of inches without measuring, at the York it is an automatic 3". Originally the targets were boards or wood shingles, often charred black and you cut an X for each shot with a sharp knife. I know of at least one shoot that still shoots at knife cut Xs on boards.
60 yards is a common range, but that can vary. Ten shots is common, but that can vary. At some shoots the big winner is the shortest string, at others there is no string, the closest shot is first, the next closest shot is second and so on.
The most common rules are these:
No false muzzles,
Rear sight at least 6" ahead of the rear of the barrel,
Rear sight can be a vee, U, or square notch only,
Front sight can be a pin head, blade, or barleycorn only,
The rifle butt can not touch the ground or be supported by anything other that the shooter,
There is no barrel length limit,
There is no caliber limit,
There is no weight limit.
This local variation is one of the charming aspects of this style of shooting for me, each local shoot has its own distinctive flavor or personality.
As to what is a chunk gun, any gun meeting the rules above could complete and I would encourage you to shoot what you've got. If the shooting grabs you, you can always move on to a different gun if you want, but shoots are not won by who shoots the best gun, but by who shoots his gun best.