Does holding a wand and speaking its command word count as V/S/M spell components?
Maybe. Depends on the requirements of the spell. Not all spells require all three. Not all material components can be replaced.
Since you're mentioning a command word, I'll assume you're talking about a magic wand like the Wand of Fireballs (which doesn't have a command word and can only be used by spellcasters, but whatever). To understand it better, let's change the context:
A sorcerer wants to cast Fireball, a spell they know. According to the Player's Handbook, pg 203, they utter an incantation (feel free to make it up), they make some sort of gesture with a hand that isn't holding anything, and the other hand grabs a bit of bat guano and sulfur from a component pouch, they expend the needed spell slot, and fireballs result. If the sorcerer can't say anything because they're in an area affected by a Silence spell, they have their hands full of daggers, or they left their component pouch at home, or they're out of usable spell slots, they can't cast the spell. Now if they have a relatively inexpensive arcane focus like a crystal or wand, they can use that instead of the bat guano and sulfur, but they still need to have spell slots, be able to make the gesture with a free hand, and say the words out loud. Using the magic wand called the Wand of Fireballs, the sorcerer would be able to save spell slots by using the wand's charges instead of their own spell slots and the material component is replaced by the wand, but the verbal and somatic components required stay the same.
Does holding the wand count as a material component for the wand's spell?
That's a really awkward way of saying it, but basically, yes. The wand replaces the material component, unless the spell's material component has a cost specified.
And if a command word needs to be used, is it considered a verbal component for the spell?
I'd say Yes. There's only one Magic Wand in the DMG that mentions a command word: the Wand of Enemy Detection. Since the effect of the wand isn't to cast a spell available in the traditional spell list, presumably the "spell" it casts is either verbal-only or verbal and material (with no somatic component).
This matters for features such as Subtle Spell, Archdruid, or to identify a spell to Counterspell.
I think you meant Beast Spells and not Archdruid.
From the Sage Advice Compendium:
If a sorcerer casts a spell with only verbal or somatic components using Subtle Spell, can an opponent use counterspell against it?
If a spell that’s altered by Subtle Spell has no material component, then it’s impossible for anyone to perceive the spell being cast. So, since you can’t see the casting, counterspell is of no use."