Let's go to the text!
True Polymorph (PHB p. 283):
If you turn a creature into another kind of creature, the new form can be any kind you choose whose challenge rating is equal to or less than the target’s (or its level, if the target doesn’t have a challenge rating).
The word "kind" seems to be pretty important here, so let's see if any other spells or other rules use it in this way:
Antipathy/Sympathy (PHB p. 214):
Then specify a kind of intelligent creature, such as red dragons, goblins, or vampires.
Locate Creature (PHB p. 256):
The spell can ... the nearest creature of a specific kind (such as a human or a unicorn) ..
Special Purpose (sentient magic items) (DMG p. 216):
Protector: The item seeks to defend a particular race or kind of creature, such as elves or druids.
Wand of Orcus (DMG p. 227):
While attuned to the wand, Orcus can summon any kind of undead, not just skeletons and zombies.
Examples we have of "kinds of creatures" are: red dragons, goblins, vampires, humans, unicorns, elves, druids, skeletons, zombies. So, that implies that that is the level of choice a spellcaster has when casting True Polymorph.
To address your examples, it seems like "elf" and "drow" are viable choices, but nothing more specific than that.
As far as physical sex goes, some kinds of creatures (marilith demons, androsphinxes and gynosphinxes, hags) are inherently constrained to specific forms, but in other cases, it's not specific to the kind of creature selected, so it's not something the caster chooses. As a DM I would generally either have the post-polymorph character be of no particular physical sex, or be of the physical sex most nearly equivalent to that of the character before the transformation.
Any other aspects of appearance are up to the DM. They might declare that polymorphed creatures bear some resemblance to their previous forms, or they might declare it to be completely random.
Also, consider this sentence from the related spell shapechange (PHB, p. 275):
You transform into an average example of that creature, one without any class levels or the Spellcasting trait.
So shapechange doesn't allow the caster to specify specifics of appearance, restricting them to an "average example" of the kind of creature they have chosen. It seems reasonable to infer the same kinds of limitation apply to the polymorph spells as well.