What grammatical function do "down" and "nearly" function as in the following sentence?
Sales of our best-sellers are down nearly 10 percent.
I believe that down functions as an adjective and nearly as an adverb.
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It is tricky to explain how "down" works in your example because it is a modifier, but the word it modifies is not there! The sentence is not wrong, per se — it is common for people to use sentences like your example in normal speech — but to analyze it, you must understand that some words are implied.
Also, as you probably know, the sentence depends on the common convention that downward movement means fewer sales.
To answer your first question, "down" is an adverb that describes the action. No specific verb is given, but I have an example coming.
For now, on to your next question. The function of "nearly" is harder to explain than I initially realized. If you look at the first version of this answer, you will see that I fell into the trap of thinking that just because it had an "-ly" suffix, it was an adverb.
Actually, it is a portion of an adverbial phrase, because "10 percent" is critical to the meaning of the sentence. Just saying "sales are down nearly" would mean something very different, and it would be very unusual to see that usage in real life because it would be considered ambiguous and awkward.
One possible complete version of the sentence is
Sales of our best-sellers have gone down by nearly 10 percent, compared to the amount of sales of our best-sellers at some point in the past.
Here, "down" is an adverb and "by nearly 10 percent" is the adverbial phrase, and both of them describe "gone."