Lohengrin 
You say:
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I was told that the rim is not from the Mexico mint.
I believe the edge looks very much like a Mexico City edge design. This comment is particularly true given the post strike damage (about average) for a well circulated but untested coin. I would ask the question of who ever said it did not look like Mexico City - exactly what was meant by that comment. It is too vague to be sure of what was meant.
At this point you should look for traces of edge milling as a step that was performed BEFORE the face images were struck into the planchet on an open collar manual screw press. The application priority, location of possible overlaps and a comparison of individual elements (lotus blooms) should be made. There are numerous threads on edge designs and how to tell if they are correct or not.
Next you ask:
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If this 8R circulated more than 200 years ago in China, shouldn't have chop marks on it?.
Actually the answer is likely NO. Silver coins once they got to China faced two primary fates. Most were melted into saycee ingots and went into storage OR they were hoarded as is. The Pillar coins were introduced into China before chops became routine for authentication. If you refer to the Bordeaux article (1915 Spink) about the forgery taking place in England at the start of the War between England and the alliance of France and Spain in 1796, you will see that Bordeaux attributes the development of chops to that specific time frame in large measure to combat the new plate technologies like Sheffield that threatened the Spanish monetary dominance in China.
Before about 1770 a counterfeiter did not have the option of making a coin with Sheffield silver plate. The technique really was not perfected as used in forgery until the late 1780s or early 1790s. So at the time this coin was supposedly made and placed in circulation (1765), there actually was no need to chop most coins.
Prior to Sheffield plate the most common method of silver coating a base metal coin was a mercury amalgam paste method or a simple wash like a paint. Those coated coins did not wear well and could be exposed (as pointed out in several sources including Riddell - 1845) by rubbing the coin on white paper. The Chinese
Schroffs also used smell, taste and feel as part of their detection routine in the time before Sheffield plate. Beyond being a bit dangerous in the case of forgeries containing mercury - the method really was effective. High grade alloys near sterling (925 fine) do have a distinctive taste not matched by most fakes. Do not try this take my word for it. The method was dropped as a recommended test in the 1960s due to health concerns.
Struck counterfeits of very late date Pillars (mostly last half of the 1760s) are known to exist. I own a few which I believe are actual Class 1 circulating counterfeits but they are exceptionally rare and usually crude. Faithfulness to the design of an actual coin is very important for counterfeit dating if you are aware of the historic time line for transfer methodologies.
Before about 1830 there was no accurate method of transferring the image of a coin to a steel die. Forgers could make molds and cast their copies but this coin does NOT look like a cast made at any time before 1830. Those early casts are very grainy and do not resemble later casts. Many counterfeit collectors avoid all casts because they mistakenly believe they are boring copies. However early molds were at times hand cut or were extensively recut because the images they produced were so bad. The premise of my theory is that the quality of the image transferred to any cast is the best way to approximate a date. Not too many Numismatic Counterfeits were made until far better casting methods were available. Remember a pillar dollar has a very small premium as a collector coin before the last half of the 19th century and at that time a coin in this state would have been worth $1.00.
So for a 1765 Pillar to be a period cast counterfeit it should NOT have such a clear image at all.
The only possibilities that remain are Modern Numismatic Forgery made with post 1830 or later techniques of die/mold replication or alternatively the coin is real.
The Pillar dollars NEVER carried a premium over silver in China as a form of commodity money either, so it would NOT be a monetary silver counterfeit from the second half of the 19th century either.
As you see, the dating process while still theoretical is based on logical straight forward theories.
Finally you ask:
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Why can we see the raised metal bits in these coins? As I understood, their presence is due to casting (counterfeit).
Logical question but to understand what the raised lumps look like on a casting, you need experience with looking at a casting in the same way you are looking at your coin. Hopefully that is with a binocular microscope. Casts vary wildly by date and the type of material used for the mold. In the last 20 years high strength plastics on the order of 20k psi or higher can be used to create long lasting injection molds or can actually be used to make strike forgeries.
What you need to become familiar with is how molds deteriorate versus how a steel die face erodes. Steel and most mold materials crack and chip far differently. Steel being much harder (over 36k psi) breaks sharply along lines of concentrated stress. It rarely cracks in a sharp curve or crosses over itself without the die face displacing. A sand cast (besides being very poor at fine details) lasts one pour. Plaster of Paris can last longer but the surfaces break up readily. This need to understand the appearance of what casts look like is interesting but complex.
I would say that the coin in question is clearly NOT a casting made prior to 1950 or so. It does not look right. But in my opinion it really does not look very cast at all. That does NOT rule out a modern numismatic forgery but makes it less likely.
The only test that can uncover modern cast copies is XRF or SEM which can detect trace elements that are either missing (gold) or heavy metal superconductors and 20th century additives like Cadmium.
I hope the foregoing is clearer than mud.
