Informally, it's known as the Nexogon.
Bricklink calls it "Plate, Modified 6 x 6 Hexagonal with Pin Hole". The part number is 27255. It's original use was as a shield in the Nexo Knights line in 2017, but it has appeared in a few other sets since then.
If you're interested in ways to use this part, New Elementary did a whole series of posts from different ...
What you are seeing is actually the result of poor lighting, somewhat worn bricks, probably camera app noise reduction, and perhaps image compression, although if you look really closely you can kinda see it's a little darker where the lettering is.
As the creator, I promise that every piece in the hat is 100% genuine LEGO pieces (no knockoff brands). ...
As pointed out by others, the first three minifigures are genuine LEGO (with the second having perhaps a few custom accessories). The fourth is not a LEGO minifig. It may include some genuine LEGO elements (legs, hands, etc), but the militaristic accessories are not LEGO elements. This appears to be a custom minifig sold at one time by Modern Brick Warfare.
I see that this popped up on HNQ, so I wanted to expand on shoover's excellent answer with a build showing one way that this could be put together for folks that may not be as familiar with LEGO elements as the Bricks community.
As was already pointed out, the key element here is the 2x2 turntable base without a turntable attached:
Here's how you might ...
These came from a number of sets, including a handy "Decorated Elements" set that covered most of the printed parts from the mid-90s space theme.
However, Recon Robot appears to be the only one that contains two of the 2x2 tiles and only one of the 2x1 tiles.
Instructions can be found in a number of places, including on Let's Build It Again.
You might be thinking they have the normal holed stud on top, which would indeed be a bit smaller. But instead what is done here is that they put the parts upside down, I think. So it's the bottom opening of the standard round 1x1 brick that you see on the top there.
They likely achieved that by using a 2x2 round tile with a stud hole as base, rather than ...
These are Panel 4 x 4 x 6 Corner Convex Ribbed
They were mainly use as decorative pieces on corners in classic space sets.
In light grey they came only in one Set: Solar Power Transporter
(photo from Bricklink)
It's 99563 LegoMinifig, Utensil Gold Ingot (Bar) in Light Bluish Grey.
Originally used for Gold pieces, nowadays regularly found as bricks and other wall decorations, for example on the ground floor of 10251 Brick Bank.
There are no LEGO parts with studs that have no logo on them. The hollow versions of studs which are on technic bricks and many other bricks have the Lego logo printed on the insides.
As someone that goes through a lot of used LEGO, I have found that there are some parts that have been worn and the logo is not nearly as visible as it would be brand new. ...
In a classic rubber duck moment, the solution has dawned on me minutes after asking the question, while browsing the list of sets owned by me to find the one that included this piece...
This is ASSEMBLY ELEMENT Ø3.2 etc. or with Bricklink terminology: Plant, Tree Palm Top:
The complete lack of markings of any kind is still puzzling, but it is reassuring ...
Picture little blurry, but this is what I see... The builder attached the tiles to Part Number Forty-Seventy.
Part #4864a, the (black) window piece is really trans-black in color, but the way it's used here, with it being reversed and all, obstructs the proper identity of the white 1x1 bricks, causing some viewing tricks on the eyes...
That is actually two parts 30351 Electric, Light & Sound Rocket Engine and 30353 Battery Box Cover. That sound and light brick was made in 1999 and only ever came in two sets.
If you look through the assortment you got you might find the Rocket Engine Nozzle that goes with it.
Image from Brick Instructions.
There are two variant of that, which look very similar:
Stud.IO lists them as:
Brick, Modified 2 x 4 - 1 x 4 with Recessed Studs and Thick Side Arches
Brick, Modified 2 x 4 - 1 x 4 with Recessed Studs and Thin Side Arches
These can be seen below, thick in red on the left, and thin in blue on the right in the top picture (not a valid colour):
Those are red technic pin connectors
bricklick pin connector
A "flick missile" pin is inserted which is one one side a bar so the minifig can hold it and on the other side a stud so the pyramid element can be placed on top.
bricklink flick missile
It's difficult to tell exactly what part this fragment came from, but it looks like it is part of a broken Technic gear or pulley. It looks like it probably came from 3736:
Your fragment looks like it was probably once one half of the center axle hole of that part.
In terms of repair, I suppose you could try to glue this back together, but given that the ...
From this image, you can count the teeth well enough to determine there are actually 60 teeth, not 40:
This does not appear to be a real part.
It also appears you aren't the first to notice this. Jim Brickkeeper had created a ShapeWays model based on this movie piece which I found while searching for LEGO 60 tooth gears. It's no longer available, but it ...
On Bricklink this is called Wedge 3 x 4 x 2/3 Cutout.
As Uli pointed out in the comments this part is called "FRONT 4X3X2/3 W. BOW" in LDD. The given image looks very similar. You can also see if this is really the part you're looking for by looking at the 3D model of it.
How I found it: Searching by properties did not work (which usually does), and I knew ...
Those horses look like legit LEGO-brand horses.
White Horse with Black Eyes, White Pupils and Dark Orange Bridle Pattern: 4493c01pb04
Black Horse with Black Eyes Circled with White, Brown Bridle Pattern: 4493c01pb02
In order to be extra sure they are genuine LEGO, look for the "LEGO" stamp on the inside of the hollow studs on their back ...