Small clarification - I favor a repeal of the Hughes Amendment, which closed the NFA machinegun registry. I object first and foremost to a law that manipulates market prices to such an extreme degree that law-abiding wealthy people can easily and freely exercise a right that law-abiding poor people can't.
These are good questions
First, for readers who aren't familiar with the 1934 National Firearms Act and the subject we're talking about ... a brief explanation. This law classified certain firearms as especially dangerous and deserving of regulation. A flat $200 tax (approximately $3500 in today's dollars) was to be paid for a tax stamp, and a federal registry tracing those firearms was created and maintained. Today, to buy these firearms, the tax must still be paid, the registry still exists, and the paperwork can take up to 8-12 months for ATF to process.
Included weapons are (broadly) machine guns, rifles with barrels shorter than 16", shotguns with barrels shorter than 18", sound suppressors (silencers), "destructive devices" (grenades, etc), and some other esoteric stuff classified as "any other weapons". In addition, destructive devices also have the manner in which they're stored regulated. You can buy a box of grenades (if you pay the $200 tax for each one, and you find can them for sale, good luck) but you can't store them in your sock drawer. An appropriate bunker, fire suppression system, etc is required.
Some historical perspective - the reason short-barreled rifles and shotguns are included is because they are more easily concealed. Initially, handguns were to be included in the NFA but that was a bridge too far for the gun control advocates of those days. So handguns were removed, but SBRs and SBSs stayed - despite the fact that easily concealable handguns were not regulated by the NFA at all. (Gun control laws don't have to make sense.)
The reason sound suppressors are included in the NFA is because hungry poor people were using them to illegally poach meals. Recurring theme: gun control is racist and classist. Most countries don't regulate sound suppressors at all, and just consider it good neighborly manners to put mufflers on loud guns.
When a NFA firearm is purchased, the $200 tax is paid, a background check is completed, and the firearm is registered. Generally, to transport it across state lines requires filing a form with the ATF. To transfer ownership to another person, another form must be filed to update the registry, and the new owner must pay the $200 tax again.
Just because something is legal to buy/register via the NFA doesn't mean it's legal in any particular state. You can't buy sound suppressors in California, for example.
In 1986, the Hughes amendment to the Firearm Owners Protection Act (FOPA) closed the machine gun registry. This meant that NEW manufactured machine guns could never be sold to civilians and added to the registry, but all of the existing machine guns in the registry could still be sold/transferred (so long as another $200 tax was paid). The result here is that legally transferrable machine guns are now extremely expensive (limited supply, no new manufacture). A semi-automatic AR15 can be purchased for well under $1000. A fully-automatic AR15 can be purchased for $25,000+ ... and some more "collectable" ones like older M16s routinely sell for $40,000+.
To answer your questions -
1.
The main point I was making was that NFA-registered firearms are almost never used in crimes in the first place, so making that law even more draconian (i.e. the Hughes amendment) was obviously not about public safety, but rather about incrementally banning a class of firearms. It was mostly a commentary about the arbitrary and incremental nature of gun control.
The NFA has a few problems with it that I object to. Subjecting all firearms to its rules would be unacceptable.
One, the tax. $200 is less onerous now, but it does still add a financial burden to the purchase of a firearm that disproportionately affects poor people. (At the time of its passing in 1934, the $200 tax was obviously meant to completely exclude all but wealthy people. Racism and classism again.) Today, $200 might not seem like a big deal when buying a $2500 custom rifle. But if you're poor and you can only afford $400 for a handgun for self-defense, another $200 is unacceptable.
Two, the registry. All of the historical data the world has observed so far is consistent with the idea that registration always leads to confiscation efforts. I want all state and federal records of firearm ownership destroyed. I'm not OK with expanding any of the existing registries to include other weapons. I don't care if the police make up some lies about how their investigative jobs would be harder without being able to trace firearm serial #s. They can stuff it in the same sack they use to keep their lies about needing encryption backdoors to all of our communications to make their investigative jobs easier.
Three, the unnecessary delays associated with the ATF processing the Form 1 & Form 4 transfers. I had to wait more than 6 months for most of the SBRs and suppressors I bought, some approached a year. The ability to exercise any enumerated Constitutional right should not be subject to arbitrary administrative delays. Freedom delayed is freedom denied. Imagine if you had to wait 6 months to get a permit to peaceably assemble and hold a demonstration. Not OK. Instant background check? OK. Eight months to cash a $200 check and issue a tax stamp? Not OK.
2.
As to which weapons should be available for citizens to own - this will always be a subjective issue, and I'll concede a line needs to be drawn somewhere. For the most part, I'm OK with where the NFA draws that line now: small arms, up to and including crew-served weapons and machine guns, some destructive devices. It's imperfect, but mostly appropriate (though again it should be noted that I object to the NFA tax, registry, and absurd delay/administrative burden).
If there wasn't already an NFA framework to build on, I would draw the line at weapons that target individuals. Any man-portable small arm that fires a projectile allows for effective defense and resistance to tyranny.
Tyranny, of course, doesn't come in the form of Army tanks and helicopters to kill you in your suburban home; it comes in the form of goons that show up at 3 AM to take you and your family away to be beaten, tortured, or quietly killed. For some reason this is a point of confusion to people who think armed citizens can't fight back against armies, despite living in a world that constantly gives us real-life examples of the ways people actually do. As well as easy examples of how today's tyrants and despots actually oppress their people. And ordinary guns are perfectly effective against those threats, for those with the will to use them.
This would exclude weapons with indiscriminate effects. Nuclear, radiological, biological, chemical, and large explosive devices obviously have no use for applications such as self-defense, hunting, or recreation. They are also not really appropriate as defensive weapons vs state actors, because of the indiscriminate collateral damage. In the Venn diagram of moral use vs terroristic use, there's too much overlap. Things like mines or autonomous weapons that aren't aimed at specific targets - no.
I think this is a useful framework for evaluating future weapons as well. Laser guns, OK. Microwave antenna area-denial skin-boiling rays, not OK. Drones with guns, maybe OK. Drones with bombs, probably not OK.
I actually think the opposition to civilian ownership of machineguns is a huge red herring. Machine guns, used by individuals are objectively far less effective than semi-automatic rifles. The military trains people not to use their rifles in fully automatic mode, because it's a waste of ammunition and less accurate than firing single rounds. Fully automatic fire has a place in squad and larger group tactics where suppressive fire is needed to support maneuver.
Most issue M4s these days actually have NO fully automatic setting, but rather are limited to 3-round bursts, because again fully automatic fire is generally wasteful and ineffective. A mass shooter with a machine gun would kill fewer people because he'd run out of ammo faster and hit fewer people with the ammunition he was carrying. One notable exception here - the Las Vegas shooter, which was an exceptional set of circumstances (distance, elevation, size of the crowd, no need to aim). And he used a bump stock, not a machine gun.
Banning machine guns doesn't make a lot of practical sense, but they are flashy, so they draw a lot of attention, despite being a non-problem.