The "1800 dollar" is a counterfeit that has been in "underground" collector circulation for many years. One of the ways to tell a real coin from a fake one is to know what the real thing looks like. Here is a genuine 1800 Bust Dollar. You second item appears to be a modern copy of what might be an anceint coin. This is not my area so one of the ancient coin experts might be able to help you further. I can only tell that the "fabric" or look of the piece is not right for that era. The "3" on the 1943 cent is very distictive. Its tail reaches down below the plane of the date. If you don't see that on a potential "1943 copper cent" you don't have a genuine piece. Here is a 1943 cent. Note how the date looks.
This selling of limited quantities of contrived rarities is the same thing as beanie babies . . . Only it’s a different branch of government doing the marketing.