I do agree with Dr Bastien, no doubt about laws, but the question is: did they really wish?
I believe that on a local level, these imitations were tolerated by officials. It would have been too much trouble to enforce these laws and, at least in the eyes of the local government, not worth the effort- all that would have really resulted would have been the alienation of the local people.
- Why the number of counterfeited coins seems to have exploded, first, nearly 318 compared to Diocletian period and the early Constantinian era and particularly in the western empire?
Imitations turn up in greater numbers after re-tariffing, like when this occurred in A.D. 318. The monetary reforms in this year de-monetized previous issues, so people made imitations out of the old issues.
- How did the authorities expect to fight the lack of small bronze coinage after the closure of Trier mint in 355, a few years after the VICTORIAE DD AVGG Q NN emission has stopped (348) and just after the Ae3 “falling horseman†was issued (354) knowing that Trier mint was providing at this time the most part of Gaul and Britain needs?
The London mint was also closed in A.D. 325, which surely meant less coins for the West, which is evidenced by the many imitations found in the Western areas of the Roman Empire. This demonstrates the lack of fiscal understanding or lack of care by the central Roman government. The Roman authorities were never that concerned with minting coins for the population. The primary concerns for a mint were minting money to pay for government debts, such as salaries of government employees and military expenditures. This is clearly shown by mint closures—the mints closed when the government officials and military were transferred to more economically important areas.
- Why is there a lot of struck imitative coins and no cast one which is probably the easiest way to produce counterfeited coinage (probably a link with Theodosian IX-21-3 code which is very clear)?
I don’t believe that people thought that they could circumvent the laws by striking coins versus making casts, especially since law IX 9:21:4 in the Theodosian Code specifically forbids “stamping.†A lot of coins, though, were cast. Kathy King (in her article “Roman Copiesâ€) has a map which shows over 120 places in the Roman Empire, with many in the West, where moulds were found that had been used to cast coins. It does seem that the majority (especially in the 4th century and onwards) were struck. I believe it would be easier and faster to strike coins once the dies were made. After making the dies coins could be struck at a very fast rate, versus the much slower process of casting.
- Why did the counterfeiters generally use a so quite similar (and expensive) alloy, as you have shown in your thesis, as the official coinage? I would have separated silver before 
.
It is probably not that easy to remove the silver from coins that you are melting down. Many of these people that were making these imitations probably had no idea how to even go about the process. Even if you did know how, it would also have probably been a lot of work for 2-5% silver. Some people did it though- in the Theodosian Code 9:21:6, it says metal casters were purging the silver, but these were probably very skilled workers who knew what they were doing, while for others the process was not understood, or they did not have the necessary supplies or material to perform the operation successfully.
But I believe that sometimes, authorities had no answer to the needs and so, if it was not degrading the emperor' s image, “closed the eyes†(at least one 
) on what was going on in a secondary territory for example. In the other hand, I have no doubt concerning a zero tolerance when it was an official transaction like paying taxes, only official coinage was accepted.
Yes, I believe the local authorities tolerated the unofficial coinage, mainly because it did not impact them. The unofficial coinage would have only been used in day to day transactions, like in the market.
