Have you purchased a firearm in the US from a licensed dealer recently? There's paper/digital record of most firearm purchase in most cases, with a few exceptions. There's a cursory background check ran too.
(In the case of most US citizens the government doesn't care about small arms. Most are used for sporting, hunting or deterrence.)
In many US states, direct private gun sales are perfectly legal. For instance, a Pennsylvania resident can directly sell (most) guns to another PA resident. They don't need to run background checks, keep records, or submit forms to the government. As long as the buyer doesn't know that the seller is a prohibited person (convicted/indicted felon, etc), it's kosher.
Because these sales aren't documented or reported, it's harder to count them. There are estimates, but I can't find anything that seems reliable. I did find an interesting article that discusses this issue at length, though:
* http://www.policymic.com/articles/24070/gun-control-policy-u...
Anecdotally, I know dozens of people who've collectively purchased many, many guns through private sales. Also, take a peek at Armslist.com, GunBroker.com, GunAuction.com, GunsAmerica.com, and similar sites.
Online sales such as all the sites you listed are required by Federal law to only ship to a licensed Federal Firearms License holder who in turn may only transfer to customers after a NICS check. So, online sales are as cumbersome as in-store purchases.
Anything with a NICS check or credit card purchase is potentially trackable.
Also, with a gun registry [proposed in various places], sufficiently smart data mining, and fast processing, it may be possible to detect an ammunition purchase [via credit card] in a caliber in which the buyer supposedly doesn't have a registered firearm.
If they are a private individual (not in the business of selling firearms) then yes. But that's no different than buying a used deer rifle from your neighbor.
However, all new guns are (since 1968) purchased from a licensed dealer, so there is always the beginning of a paper trail. How far that goes before it gets muddled in private sales is another matter.
My understanding is that there is technically an exception to this where you can manufacture your own firearms so long as you stay under the yearly limit and do not manufacture them with the intent of distributing them. Once you have done so, you can then distribute them as a private citizen.
That reads weird because the legality of distributing it depends on if you can assert that distribution was not your intent when you made it. This means this is probably not a very practical exception, as it potentially involves you arguing something rather nebulous in court.