Reversible hat

The fabric hat is reversible so you can a brown or red hat 

I would hazard a guess that the hat is a medieval style, the kind that would normally be made from wool.

The hat is basically a square bag, that follows the shape of the head when worn and leaving 4 corners at the crown where there is an air pocket above your head.

Many shapes of historical hats do not have names, you could call it a beanie of shorts

I would say this hat suitable for any period from at least the 13th to 18th century. 

Mob Hat

 A Mob hat or cap was worn by Georgian women of any status. 

Its also called a Mop cap which is probably due to a subtle change its use from a frilly bonnet to a hat used by victorian maids who mopped the floor.

This style of hat is mainly associated today with Victorian maids and would normally be white.

Basically, a round cloth gathered with a ribbon or string to give a ruffle brim and covering.

Designed to keep the hair under control, modern plastic and net variants are used in clean environments such as food factories for the same reason.

These caps or a version of them were worn by men at least in the early 18th century but were predominantly women headwear.

Gold Fascinator

This hat was described as a Theatrical, Wedding, Gold, Empress Style. Medieval Reenactment Hat, Fascinator.

Fascinators usually are something associated with women's headwear rather than men's and are basically a hat that covers only a small portion of the top of the head and purely ornamental in function.

While possible designed for a woman, I can see easily being worn by a man

This fascinator is made of lightweight wire gauze, with trimming  

It could be used for an Arabian or East Asian Princess or Prince

 

Cheap Chinese Style Hat

 This hat is about as cheap as they come and even as a novelty hat not recommended

Mimicking some other watermelon style oriental hats, this is made of some cheap fabric over some thin foam, that both makes it uncomfortable and a poor fit. The shiny fabric is slippery and this makes it readily just fall off your head, no matter how tight you pull it down

I have a similar hat here and although also a novelty hat far more comfortable and better made