You know how our real hair shines and looks lighter in sunlight? My hair is black and when light shines on it, it shines brown. How will, and how well will the hair piece I order replicate this effect?

Ha!, half us wearers complain the hair is too shiny and half of us complain its too dull!

They tend to start off shiny when they're new, but obviously the hair isn't being fed any natural oils or supplements, so it dulls over time.

Using small amounts of product in the hair can maintain or restore the shine.
Even something simple like brylcreme can achieve that.
But its wise to never over do it because too much product can have a negative effect on the look and oils that get down to the base can weaken the attachment.

What I also think you're referring to is is the 'tone' that hair can take on in different lighting conditions.
Ideally, the factory will have matched your hair sample and the replacement hair will reflect light the same tone as your natural hair does.
But in many cases it doesn't always work out like that.

Again, using hair grooming products can help because they 'mask' the hair and then it all reacts the same way in lighting.
But you can also use products like colour conditioners that will maintain the overall colour, but unify the tone.

I am only referring to what your calling "tone" or how hair shines lighter in color when light hits it, in my case from black to brown. Am I really at complete mercy of the factory for getting this natural and beautiful feature? How often do they not get it right? You see, I have no experience with hair products of any kind and don't know what to expect from a hair piece at all. The gallery of pictures looks somewhat promising, but I thought I ought to make sure the factory is aware of this characteristic that is visible in natural hair.

The factories are meant to analyse your hair samples under a microscope.
You'd be best to supply different samples from different areas of your head so that it replicates your own hair as much as possible.

Hersute is correct. Samples from various areas of your head is helpful. There can be more 'tones' to you hair than you realize. The sunlight affect that you describe is exactly why synthetic hair doesn't cut it. Synthetic hair looks great in your hand--it's extremely realistic. But mix it with your own human growing hair and step out into the sunlight and the difference is a dead giveaway. The factory will match your hair color exactly under a microscope.
John