One is a bullet measuring .58. I have never seen this one before.
The other is a Rosette, I believe, but not military?
The third item is very strange. It is brass and appears to have saw marks cut into it vertically. The landowner suggested it might be a part of a powder scale?
Your bullet is called a williams cleaner bullet. That is a zink base that would be pushed into the bottom of the bullet and force a thin brase skirt to come out and clean the barrel of the gun.
Your guess is correct, the large disc is a civilian rosette from a horse-harness.
Taz420 is of course correct, a Shot Flask top.
Duggap is also correct, it is a civil war era Williams Type 3 "Bore-cleaner" bullet (which was manufactured only by the yankees). The flat disc on its base was made of "hardened-lead." The disc held a thin zinc saucer-shaped washer onto the main lead bullet's base. When the "Bore-cleaner" bullet was fired, the base-disc compressed the saucer-shaped washer outward into the gunbarrel's rifling grooves, scraping out the burned gunpowder ash.
The shallow groove encircing the top of your Wlliams Type 3 bullet was not there when the bullet was manufactured. That groove was made by the rifle's ramrod or a double-helix bulletworm.
Wow thanks for the invaluable info guys! This site never seems to run dry and never disappoints. I find lots of Springfield and Henry rounds along with a few others but have never came across this Williams. Thanks to Tax420, duggap and Cannonball Guy for the great ID's. I will mark this one solved.