Why do I do this to myself?! I am NOT a seasoned birder, and my only marginal expertise is in dead seabird identification. Live shorebirds? What was I thinking?
Anyway, I am fortunate that our usual pros weighed in on this one: John Stanton and Mary Wright wrote in with answers. First, the easier ones, on which Mary and John were in agreement: Birds B and C are both Piping Plovers. Bird B is an immature bird, while C is an adult. Kathy Kelly, who photographed the birds, tells us that she spoke to Eric Hynes, staff naturalist with Maine Audubon, who told her this young bird was one of two that hatched on Pine Point Beach. Its sibling went missing, and was likely lost to predation. He told Kathy this Bird B was just about ready to go off on its own.
While the markings on the immature and adult birds do differ, there are certain characteristics common to plovers generally that we can focus on for the purposes of identifying Bird A, which is a thornier problem.
The general look of a plover is a large-eyed, straight-beaked, and somewhat dome-headed bird. Someone once described their very high foreheads as giving them the look of a dolphin, and that description seems apt to me.

Bird A: Mystery plover?
Bird A appears to be a plover, but what sort? Mary says Killdeer, and John says Wilson’s Plover. I’ll throw another common species into the mix and say Semi-palmated Plover just to make things interesting. The view in the photo is from the back, and with the head turned away, it’s hard to get a good sense of the size or length of the bill. So what can we say about this bird? It has a distinct white collar above a brownish-gray back, a brownish-gray head and a pale supercilium (“eyebrow”). The legs appear to be orange, at least to my eye. What we can see of the bill is black.There is no evidence (from this angle) of a strong black band encircling the upper chest/base of neck, which is common in many plover species.

Killdeer--even from this angle, the double breast bands are evident.
Let’s consider the Killdeer as our first candidate. Killdeer are rather lanky for plovers, and that’s very consistent with Bird A. Back color works for Killdeer, as does the pale supercilium, white collar and black bill. What argues against Killdeer is Bird A’s orange-ish leg color, and especially the apparent lack of any black breast bands in our bird. Even when viewed from a similar, oblique angle, Killdeer of any age and sex should show some portion of the distinctive double breast band that sets them apart from other plovers. The photo here of a Killdeer from a similar angle shows the upper breast band encircling the entire neck at the base of the white collar, and the second, lower breast band extending all the way to the “wrist,” or forward bend in the wing. Bird A shows no trace of either.

Non-breeding Wilson's Plover: heavy black bill is distinctive (when you can see it.)
How about Wilson’s Plover? Unfortunately, perhaps the most distinctive feature this species is a long, heavy black bill that sets it apart from otherwise similar plovers. The angle we have on Bird A makes it tough to say much about the bill, but it doesn’t look terribly heavy, from what we can see of it. Wilson’s Plovers generally have a sort of dull gray-yellow leg, a grayish back, white collar and a pale supercilium. Breeding adults have a single black breast band, but juveniles and non-breeding adults have a washed out looking gray band, which could account for the lack of any evident black breast band. Perhaps the biggest problem with an i.d. of Wilson’s Plover is its location: these birds typically breed from Virginia south, and while occasional sightings are not unheard of in New England, if we’re playing the odds, we’d have to bet against Wilson’s Plover.

Range map for the Wilson's Plover. Summer range in pink.
And what about Semi-palmated Plover? Well, if you accept my premise that Bird A’s legs are orange(ish), then that’s a strong point in favor of Semi-palmated Plover. And non-breeding birds have less of a distinct black breast band, and more of a grayish band that blends into the color of the bird’s back. The white collar is consistent with Bird A, as is the pale supercilium. This is by no means the clear and final answer, and I would be delighted to hear from John, Mary, or any of you on how you go about plover identification. As for me, I have exhausted myself trying to work through this, so I think I need a nap.

Semi-palmated Plover. Are orange legs the key to Bird A's identity?