I think you coin has suffered severe environmental damage. I note what looks to be small bits of corrosion in some of the hard to clean areas on the reverse. It is surly not any type of error coin. IMO.
The rear of the coin shows evidence of a grease strike through. 1) "e pluribus u" is more unclear than "num". Each letter becomes progressively more defined with the beginning of the motto being nearly invisible. 2) The first and last letters of "UNITED STATES" are weak with stronger letters in the center. Both are evidence of a strike through on the reverse. The front could be a very severe strike through. The fact that there is evidence of strike through on the reverse makes it more likely the obverse could also have been struck through grease. The weight is the evidence against a strike through. It's lost a lot of weight and this points towards wear and/or other damage. I don't think you will ever know for sure but I'd say there's a 60% chance it's a strike through and 40% chance it's wear and damage.
Interesting Cent. With that weight it's most likely PMD IMHO If it were struck through grease, trial strike or capped die strike it wouldn't be that much less weight.
If it was capped, wouldn't the reverse be in much better condition? It seems that the reverse is also damaged.
Sorry, I cannot tell anything. First coin on the left may be a cap. I didn't see the coin in the OP. I was looking at the three different coins. I think the coin in the OP is an alteration of some kind. If it is larger than a normal coin, I heard you can make one using two piceses of rubber and a hammer.
I do not have a caliper to measure the diameter, but it is exactly the same size of other wheat cents. I am posting an image of the cent with the light at a different angle. (my thumb is at 5 o'clock)