Not much.
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.
Short answer: Yes you can, but it could get complicated
Addressing the elements in reverse order:
The Soul of a Warrior Trapped in a Toad's Body
Can a character True Polymorph into itself as a means of reversing a True Polymorph someone permanently cast against them earlier? (ex: A warrior is permanently transformed into a toad. The party wizard shows up to permanently transform the warrior back into his regular self.)
First of all, his equipment's gone if you turn the toad back into a warrior.
p. 283 PHB, from the spell description.
The target’s gear melds into the new form. The creature can’t activate, use, wield, or otherwise benefit from any of its equipment.
Secondly: what is the CR or character level of the toad? When he got turned into a toad with the one hour concentration that made it permanent, that new form has new statistics, and has either a level or a CR bounded by how the spell operates.
the target's game statistics are replaced by the new form statistics including also its mental ability scores ...
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).
If your warrior was ninth level, did he become a ninth level toad, a CR X toad, or what? As a point of reference: a Giant toad is CR 1, a Giant Frog is CR 1/4, and a regular frog (close enough to a toad) is CR 0.
Once the level or CR of this toad is established (work with your DM) you can transform that "once a warrior, now a toad" into a warrior (himself?) with a CR equal to or less than the CR of its current form per the spell description.
There is a potential for bad news: what is the equivalent level of a CR=0 warrior? A congressman?
The target’s game statistics, including mental ability scores, are replaced by the statistics of the new form. It retains its alignment and personality.
That last sentence opens the door to "kiss the frog and restore the prince inside." If who you are is made up of your alignment and personality and your soul (you aren't dead, you are alive, it is YOU in there, and souls* are part of D&D 5e), then "You the toad" could be a level-X warrior trapped in a toad's body.
Your DM could rule yes or no on that.
- If DM rules no, it might take a wish spell to restore the warrior to
his true self.
- But DM could rule yes based on the soul of the warrior remaining intact due to still being alive, albeit in a new form.
*Note on the soul, from 9th level Astral Projection spell:
If the cord is cut—something that can happen only when an effect specifically states that it does — your soul and body are separated, killing you instantly.
From this we deduce that while still alive, your soul -- who you are -- remains with you regardless of what form you are in. There's hope. "Who's inside that new body?" is also addressed here in the section with the title "The Vibe."
Now for the Generic question:
Who's Really In There, Inside that Body?
Can a character True Polymorph into itself (possibly after transforming into some other form first)? Possibly to prevent aging, cure wounds, or alter their original body in some way?
Once the CR/Level issue noted above is resolved with the DM, yes, as long as whomever casts the spell can concentrate long enough to do it. Once again:
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).
Work that out with your DM and proceed.
For what it's worth, Jeremy Crawford(lead rules dev for 5e) had this to say about who is in there:
A spell doesn't erase/suppress your memories unless the spell's text
says it does.
When the text of a spell, like polymorph, says you retain your personality after a transformation, that's a terse way of saying, "You're still you, despite the radical changes you undergo." #DnD
Supporting point on it being "you" in there no matter what form you take.
There is a hint that "it's you in there!" in the "Creature to Object" element of the spell (p. 284 PHB) where a creature becomes an inanimate object for a while (not a permanent transformation). "You" are in there but "...the creature has no memory of the time spent in this form ..."
This can be read as being due to inanimate objects having no mental abilities. (Remember, the new form's stats are now your stats). You were in there, body and soul, but the lack of mental traits rendered memory irrelevant ... more "in a coma" than "brain death." You come out of this "coma" alive and intact, with your stats, when the spell expires.
This interpretation, you not being dead when temporarily an object, is consistent with soul and body being bound together in a live character, however impaired in terms of stats.
If the change into an object is permanent ... that's another story, or another trope.
Work with your DM.
Best Answer
Even though this is a homebrew spell, I think the question should be able to be answered from the rules and come to an applicable conclusion. That being said, all the normal caveats about homebrew material apply.
I am adhering very strictly to RAW (to the point of being over-strict possibly) due to your DM's ruling policy and your request.
I'm going to assume in my argument that you are only trying to create the actual ink and not also a bottle to hold it in.
Definitions
Definition of object:
Note on this definition D&D5e likely specifically left this definition vague so that DMs could and should decide for themselves what is an object and what is not. Thus, this is almost always going to boil down to DM fiat at some point. However, RAW does offer some guidance beyond just that.
Your DM is technically not following RAW by disallowing objects with multiple materials
Objects composed of different materials are still considered one object
The good news here for your argument is that there are things in the definition that are obviously composed of more than one piece or material and still considered a single object (a window for example). A musical instrument, some of which can be very complex, have also been confirmed to be a single object by Jeremy Crawford. Dead bodies are also single objects (more on this later).
So, your DM's current method of counting different types of molecules as different objects really does not hold weight with the rules.
Strict RAW - TP can't create ink because ink is not discrete
Objects must be discrete
However, we run into a problem right away when it says "discrete".
Liquids are, by their very nature, not discrete. Discrete objects can be easily distinguished and separated from other objects. For example, if I put three different colored ice cubes in a bag and shook it up, I could open the bag and still see 3 different ice cubes and point them out. If I put them in a bowl and let them melt and mixed them up there would be no way to separate them. Thus, ink (and liquids in general) are not discrete. And thus, ink would not be a legal target or result of true polymorph.
So, by this very strict reading, making ink via true polymorph would not be allowed.
In some ways this actually makes sense. If you saw a puddle of ink on a desk would you consider it "an object"? Probably we would more describe it IRL as a substance actually. Regardless the rules are what they are.
Possible things to try
You might be able to get around this by creating a bottle of ink, which, as a whole, would be considered discrete. However, would likely run afoul of your DM's interpretation of how you separate objects out.
Some inks can also come in solid form so maybe you could try that as well.
However, there are possible counterexamples/contradictions
Acid, Oil, and Holy Water
Despite the definition above, the rules specifically allow vials of acid, holy water, and oil to be used as improvised weapons.
The improvised weapon is important in this case because an improvised weapon requires an object:
A bottle of acid and ink (or a bottle of ink) are similar enough to say that if one can be considered an object, so can the other.
Dead bodies
Also of note is that dead bodies (!) are considered to be objects by the rules. And bodies are composed of many different and varied materials and a LOT of fluid. This creates the interesting ruling that if you hold to strict RAW, any spell you cast on a dead body would not affect the blood, bile, urine, etc. inside the body. This makes no sense and it is not clear what would happen to the body and/or the fluids in the case of a spell affecting the body.
So, if a dead body (composed of lots of materials, essentially just a sack holding a bunch of liquid) can be considered an object it might not be unreasonable to say that ink could be as well (or even a bottle of ink).
If you are going by strict RAW, your answer might just be "no" unless you can convince the DM that these counterexamples make a compelling case for the game intending this to be allowed.
It is possible that your DM has other motives
If your DM created this spell and has a specific spell component in mind, maybe he is using this as some sort of plot hook or interaction hook on purpose and that is why he is limiting you in this case. Worth checking to make sure you are understanding each other.
Regarding spell components
(I still think this question deserves its own question but I'll make a pass at answering it here)
Obviously, if you follow the strict RAW above, anything liquid or gaseous will not be able to be created because of the "distinct" issue.
You can't create living plants because they are neither creatures nor objects.