It's kinda hard to tell much without a picture.  Reamers are listed in
the 1911 Mack (D.R. Barton) catalog, square, octagon, and wood reamers.
No picture, though, of the wood reamer.  The square and octagon reamers
are bits for braces, and I assume the wood reamers are as well.

As a class of tool, they can be handled in a number of ways.  Some are
designed for use in braces, some can be mounted in handles like pin
vises, some are T handled.

> 1)what trades habitually used these little reamers, and for what?

The square, hexagon, and octagon reamers are for metal workers. There
is a reamer built like a spoon bit that was used by plumbers for
tapering a hole in lead pipe to join one pipe into another -- like
a T joint.  These are quite short and wide at the top.

What you seem to describe, however, is a wood worker's tool and most
likely used by chair makers.  It seems too small for tap augers, which
are usually at least 1" in diameter at their widest point.

These can be used to relieve a hole, or to drill a tapered hole from
the start.

> 2) What kind of handle would they have had? Mounted in a brace,
> cross-handle, tap wrench, or handle along the axis like mine? Are
> there other possibilities?

I have two, tap augers, and they are mounted with a T handle.  I have
another that is designed to be used in a brace.  All are larger than
what you describe.

> 3) How sharp should they be, and how are they sharpened? Mine are dull
> enough to run a finger along the edges with a fair bit of pressure.
> There is no sign of a bevel from sharpening with a stone resting
> edge-to-edge, and no sign of a bevel running down into the hollow. No
> signs of sharpening at all, in fact.

Regardless of intended use, these need to be sharp.  The one I have
that is designed for a brace is sharpened by rubbing it flat across
a stone.  The cooper's tap and bung augers I have (and have seen)
are sharpened a bit more radically, and require careful work with
a hard file or a slip stone.