I'm anticipating that someone will tell me I won't really know what
the color will look like until the test pieces dry. That brings up my
second question: How long will the dye solution be usable after it is
mixed? Hours? Weeks? Months?

You don't know how it will look until it is varnished (or whatever). Dyed
wood changes pretty dramatically.

Since you are talking about drying, I assume this is water dissolved dye. I
have been using some I made up 2 years ago with no problems. Haven't any
idea what its actual life is, but certainly long enough for your project.

I make up a test solution. Add a little more A, dilute it some, add some B,
etc. until I get what I want, and then just use it. The bottle makes up so
much that I have no concern about wasting it.