Shotguns have been used throughout military history. The forefather of the modern combat shotgun would be the blunderbuss, a short barreled, large caliber musket which would be loaded with shot. These handy weapons were popukar with those who needed a handy lightweight bit of firepower, like cavalrymen, or people who expected to be fighting in close quarters, such a naval boarding parties. "Buck and ball" musket loads (a musket ball with some buckshot poured on top down the barrel", saw a lot of use durng the American Revolutionary and Civil War conflicts. Generally, shotguns were a civilian weapon for hunting, and were therefore found amongst militia forces or similar organisations.

The advent of the first military issue shotgun came with the end of the 19th century. Due to the first pump action and semi-automatic shotguns appearing in the the US at the time, the US military were keen early adopters, deploying them to confilcts such as the Phillipine-American War. These were generally not "combat shotguns" per se, as weapons manufacturers did not yet properly distinguish beween the pump action shotguns sold to civilians, militaries and law enforcement agencies. This did not deter interest however: American police forces were quick to appreciate the enhanced firepower pump-action "riot guns" provided to officers, and also their ease of use and versatility, being able to fire a wide range of ammuniton types.

The birth of the first true combat shotgun came with the US entry to the First World War. Lack of experience in trench warfare showed in the freshly deployed American troops, and urgent calls were made to equip these troops with more suitable weapons, and the Trench Gun was the result. Winchester took their extremely successful pump action models and produced the M1987 and M1912 model of trench gun. Instead of just being off the shelf models, these were weapons specifically redesigned for close quarters combat with shortened barrels, perforated heat shielding on the barrel and bayonet lugs. They also retained the lack of a trigger disconnector, a device that prevents the weapon firing while the slide is pumped with the trigger depressed, allowing a whole magazine to be expended in a few seocds, known as "slam firing". Firing 12 gauge antimony hardened buckshot shells, the Trench Guns gave US soldiers a devastating edge in trench combat, so effective the German government actually lodged a formal complaint against the weapon, labelling it inhumane.

Question 1: How much were shotguns used

This is a bit subjective, but its safe to say they've been used since 1900 and even long before. Both the Winchester Model 1897 and Model 1912 were used as combat shotguns during the First World War. The Model 97 was used up until WWII in smaller numbers and the Model 12 was used through Vietnam with the Ithica 37 taking its places when production ended in '64.

There were also a number of other manufacturers to supply pump action shotguns to the military during the 20th century. Remington, Savage/Stevens, and Mossberg in addition to those previously mentioned all produced various models that were sold to branches of the military.

Question 2 and 3: Semi Automatics

As shown in "Making a Gunner" a 1943 US Army Air Forces training film, semi automatic shotguns were used during WWII as a training aid to teach gunners the concept of leading the target. The Remington Model 11 and Savage 720 (both licensed copy's of John Browning's Auto-5 design) were used for this role.

As far as actual use of these shotguns in combat, I'm not 100% sure, so I don't want to speculate. There were prototype trench gun variants made of the Remington 11 at the end of WWI but it was never adopted as the recoiling barrel was an issue for bayonet mounting. They did however serve as prison guard/crowd control weapons used by the military.

The range of a shotgun is determined by the type of shot/projectile used and the choke constriction in the gun. While felt recoil is subjective as well, from personal experience my 12 Gauge shotgun does not feel that much worse than shooting an M1 Garand or other full size combat rifle of the WWI or WWII era.

The Pancore Jackhammer is a real weapon, though it was not produced commercially. Ian at Forgotten Weapons can tell you more: https://www.youtube.com/watch?v=-VKGhqIl4Gw but in a nutshell it was a prototype that failed to take off and get military acceptance. It was used commercially for movies, video games, etc. after that.