What subatomic particle is a black hole composed of? 
*

*In a black hole, what is the "state" in which the mass that is present is in? 

*Are they there as tightly packed neutron or soup of quark or are particles broken down into 10D strings and coiled as tightly as possible. I read that white dwarfs are just closely packed neutrons.

*Additional question - What is the "volume" of quarks?
 A: I can give a layman's answer

In a black hole, what is the "state" in which the mass that is present
  is in?

It's often suggested that black holes shrink to a finite point, or to the size of an atom or quark, but it's impossible to know without a model for quantum gravity.   
In layman's terms, gluons, which, kind of, give protons and neutrons their structure, travel at the speed of light, so they can't travel away from a black hole, which suggests that there's no process by which the material inside a black hole can expand, it can only contract and as it contracts the gravitation continues to increase - hence, the "it shrinks to a point" argument.  
But because we don't know, there's all kind of fun theories like a black hole is a portal, a wormhole or it houses an entire universe.    I personally consider that more fun speculation than good science, but the simple truth is, we don't know what happens to the material inside a black hole.

Are they there as tightly packed neutron or soup of quark or are
  particles

That would be a Neutron star.   Quark Soup or Quark Gluon Plasma has been discovered at CERN and could exist inside Neutron Stars.

Source, Wikipedia

broken down into 10D strings and coiled as tightly as possible.

That's also uncertain.   10D string theory works mathematically, but it's far from an agreed on theory.   
As to "coiled as tightly as possible", I think it's a mistake to try to apply what we physically understand to the quantum world.    Under high pressure, we expect things to get packed tightly, and to an extent that's true, but what actually happens (We don't know what happens), but what ever actually happens might be stranger than simple compression.

I read that white dwarfs are just closely packed neutrons.

That's not true.   A white dwarf isn't dense enough to squeeze protons and electrons into Neutrons.    A Neutron star is sometimes described as "just closely packed neutrons", but that's not a good definition cause it's not true.   It's surface is super-dense atomic structure of sorts, it's lower-mid levels are neutron rich but not entirely proton and electron free, and it's inner core may be more of a soup of quarks than neutrons, though it may be close to the Neutron ratio of 2 Ups to 1 down. (May be - I'm not sure).
A: One way to think about this would be to connect density of infalling matter to length scale and energy (think along the lines of natural units). If we assume the simplest Schwartzchild Black Hole, as matter approaches the singularity, the density of that matter will increase. At some scale (when the matter is somewhat close to the singularity), the density of the inflating matter will surpass nuclear density. As the matter continues to approach the singularity, the density of matter will pass the density of the universe at the time of the electro-weak phase transition. (In short falling in towards a black hole includes increasing density, which is similar to going back in time in the history of the universe.) 
Presumably at some level, the density of the infalling matter will be comparable to the density of the very very early universe. When this occurs, all the important particle physics processes and quantum gravity effects that were present in the early universe will be on display (although unfortunately I can't tell you what those are, exactly). See, for ex. https://arxiv.org/abs/gr-qc/0604072
A: I believe a short answer to your question would be that we don't know, and we can't possibly observe it, since the mass you're talking about exists beyond a singularity, meaning that any attempt to reach it would take an infinite amount of time. You may be asking a different question, however, what does string theory suggest is the "state" within the black hole (I assume you're looking for an answer relating to string theory from your mention of 10D strings in your question), and that, I can't accurately answer. Maybe someone more familiar with string theory could add to my answer.
A: 
In a black hole, what is the "state" in which the mass that is present is in?

Subatomic particles belong to the realm of quantum mechanics. A black hole is a general relativity object and once it forms it attracts all matter which, once below its horizon, cannot get off. So it will depend at what distance from the classical singularity and for what a mass of a black hole one is asking this question.

Are they there as tightly packed neutron or soup of quark or are particles broken down into 10D strings and coiled as tightly as possible. I read that white dwarfs are just closely packed neutrons.

It will depend on the density and energies of the subatomic particles falling into the black hole.
At the first formation, if it starts from a neutron star it will be closely packed neutrons and closer to the singularity ( higher pressure) quark gluon plasma will be formed . The answer to this question covers the process:

When you talk about a black hole with a stable mass (at least 3 solar masses), it is good to consider that they come in 4 flavors: rotating-charged, rotating-uncharged, non-rotating-charged, non-rotating-uncharged.
What we would see visually during the transformation would be a hard radiation flash. This is because during the collapse, the particles on/near the surface have time to emit hard radiation as they break up before going into the event horizon; so this could be one of the causes of gamma ray bursts (GRBs).
We know that atoms break up into protons, neutrons, electrons under pressure.
Under more pressure, protons and electrons combine into neutrons.
Under even more pressure, neutrons break down into quarks.
Under still more pressure, perhaps quarks break down into still smaller particles.
Ultimately the smallest particle is a string: open or closed loop, and has a Planck length, which is many orders of magnitude smaller than a quark. if a string is magnified so it is 1 millimeter in length, then a proton would have a diameter that would fit snugly between the Sun and Epsilon Eridani, 10.5 light years away; that's how big a proton is compared to a string, so you can imagine there are perhaps quite a few intermediate things between quarks and strings.

So it will all depend on the developing theory of quantum gravity, on what exists at the singularity.
After the initial formation the hole attracts near by masses, and the process of assimilation will be analogous to the one above, until the singularity is hit where quantized gravity is needed to really model what is happening.

Additional question - What is the "volume" of quarks?

Quarks have no volume, they are point particles in the lagrangian of the standard model of particle physics.
A: Actually we exactly dont know what it is made of.But according to me its made of the same atoms as other atoms present on aur earth,sun etc as all the stardust only goes inside it.Yes, it can be such that it may be  under high pressure  and temperature that it would break into ions and all.
It was a nice question.
