Short answers, pulled from the story.
The Agar gun was nicknamed the Coffee Mill Gun because its hand crank and funnel-shaped ammunition hopper gave it a strong resemblance to a common kitchen coffee grinder. The hopper sat on top of the weapon where loose cartridge tubes were dropped in and fed down into the firing mechanism.
Yes. Lincoln witnessed a demonstration of the Agar gun at Washington Arsenal in 1861 and was so impressed that he ordered all ten available weapons purchased the same day at $1,300 each. He wrote that the gun was "worth the attention of the Government."
The Agar gun's rate of fire was capped at 120 rounds per minute. The limit was deliberately imposed in part to prevent the single barrel from overheating during sustained use.
The Agar gun fired .58 caliber cartridges. Paper cartridges were loaded into reusable metal tubes, each fitted with a separate percussion cap, which effectively created a centerfire cartridge before that design became standard.
Confederate forces captured seventeen Agar guns when they took Harpers Ferry in September 1862 and used them sparingly in 1864. The guns entered Confederate service through capture rather than manufacture.
The Ordnance Department condemned the Agar gun for consuming too much ammunition to be practical. It also suffered from overheating, jamming, heavy and easily lost steel cartridge tubes, and a range of only about 800 yards, which was no better than a standard infantry rifle-musket. The remaining guns were sold off in 1865 at $500 each.