Well thank you for the disclaimer, seeing as virtually everything you posted is incorrect.
In the United States, various items fall under the National Firearms Act, and are considered to be NFA items subject to registration by the ATF. These include suppressors, machineguns, destructive devices, short-barreled rifles, short-barreled shotguns, and Any Other Weapons (pen guns and small shotguns, mostly). "Class III" is an incorrect term, actually referring to the type of license that's held by the dealer selling the items. There is no such thing as an individual "Class III license" to buy and own NFA items-you simply must pay $200 every time an NFA item changes hands. Armor-piercing ammunition is regulated seperately, and high-capacity magazines aren't regulated at all on a federal level.
As far as purchasing goes, the process basically involves filling out a couple of federal forms, submitting a $200 check to the ATF, and waiting a month or two for approval to come back. In some areas police chiefs will sign off on NFA items, but most people simply elect to form a corporation or living trust, and buy them in the name of the legal entity (thus avoiding the need for a law enforcement signoff). Silencers/suppressors (despite what the pedantic say, the terms are interchangeable) generally run from about $300 up to $1000, with a very few specialized rifle suppressors running past $2000. Overall, the process is fairly simple to complete, and anyone with a clean background who lives in a state that allows silencers can purchase one pretty easily.
Presently, there are tens upon tens of thousands of legally owned silencers in the United States, owned and enjoyed by firearms enthusiasts and sportsmen across the country.