ReqForHelp: Understanding Vf relationship to supplied V and A
Could someone help me understand if the Vf I measured is a 'static' thing? I mean, is Vf just Vf no matter what or is Vf dependent on what voltage is supplied to the LED or what current is being supplied? 




Figure 1. Small LED current versus voltage curves. Source: I-V curves.

LEDs are non-linear devices. They don't have a linear relationship between current and voltage (I-V) as in the case of resistors. Rather, the current increases exponentially with voltage. If an I-V curve is available you can predict what current will flow at a given voltage.



Figure 2. Variation in \$ V_f \$ (forward voltage) for the Cree LTST-C170TBKT white LED. Source: Variations in \$ V_f \$ and binning.

Because there can be a wide variation in \$ V_f \$ it is generally not a good idea to directly parallel LEDs as the currents through them will then vary significantly. For low voltage applications a series resistor with each LED will help to balance the currents. For higher voltage applications series connection of the LEDs ensures the same current through each.


  The second sends 54.5 mA at 2.57 V. The third sends 11.75 mA at 2.28 V. The first two are "bright" and the last is "dim". I can't see any brightness difference between the two 2.57 V settings even though the A is different.


The currents through the first and second are too close to perceive a difference.


  In the highest current setting (54.5 mA at 2.57 v from the board to the entire LED panel) I measured the Vf across one LED, getting a measurement of .986 V.


There's something wrong there. You are unlikely to be able to see any light at that low voltage. Try measuring again.


  Did I measure a Vf number that is useless to me if I want to use a 3.3 V supply or a 5 V supply? Apologies ahead of time for my thickheadedness, but I just can't make sense of all this.


3.3 V is low for white LEDs. (See the binning article for more on that.)

The linked articles are mine and may help your understanding.