I'm somewhat ignorant about reloading costs. Without accounting for the cost of the non-consumables such as the reloading equipment and tools; is it cheaper to reload/hand load ammunition vs purchasing a box of ammo off the shelf for common ammo types for rifles, pistols, and shotguns such as 7.62mm, .223, .308, 9mm, and 12 gauge? If so (or not), about how much is the difference between reloading and store bought?
It depends on exactly what you're loading, but generally, yes. In 9mm, I can load 115 gr. plinking rounds using plated bullets for about $.19 per round, which is about $.05 cheaper than the lowest store bought. If I'm loading 158 gr. subsonic, though, my cost goes up to about $.21 but store bought goes up to about $.38 per round. For .300 AAC Blackout subsonics the difference is even more dramatic, about $.50 a round to reload vs. $1.25 to $1.50 a pop for store bought, if you can even find it. At that rate a few trips to the range go a long way toward recovering the cost of the press and other equipment.
Reloading is also becoming more economical than it used to be for military calibers like 5.56x45mm and 7.62x51mm as the supply of cheap military surplus ammo has mostly dried up.
And of course if you shoot anything exotic, including anything with black powder, reloading is an absolute necessity.
On a less related note, is there a method out there for a private citizen to easily reload rimfire type cartridges such as the .22 LR?
No.
As to the original question, for a while loaded ammo, bullets, and primers were also impossible to get, but those bottlenecks seem to have cleared, leaving powder as the one component you can't find. Powder is coming in, it just flies off the shelf faster than it arrives. You can set an alert or backorder at a lot of online stores, but the cost of hazmat shipping makes that an expensive route unless you're buying a lot at once. The best thing is to have a friend who works at a gun store.