Is there anything actually inside a black hole, do they actually exist? When objects fall into a black hole, observers outside the black hole will never see the object cross the event horizon because the object's time slows down and will stop at the event horizon. The object also become red shifted until it is no longer visible. I read that that from the perspective of the object falling in that time goes on as normal and it falls through and no special place like the event horizon is apparent, eventually it reaches the singularity in infinite time. 
This all makes sense when talking about a classic black hole where the black hole will last forever. As long as we don't see the object any more, what ever happens to it happens to it. Information is not lost but just stored in a black hole forever. 
However, when talking about black holes with Hawking radiation. The black hole will evaporate before the object reaches the event horizon. If anything actually falls beyond the event horizon, there comes out the black hole information paradox. The paradox is remedied by saying all information that falls into a black hole gets represented at the surface of the event horizon and the hawking radiation interacts with the hologram to retain information so it is actually never lost, the holographic principle. This means everything that ever fell in would be represented at the surface and just frozen there. 
Obviously a person falling in will get rearranged and die but it seems to me that a quantum observer who falls in the black hole will just come out as hawking radiation. This just means that a black hole is not a singularity and simply a quantum object that distorts spacetime a lot at the event horizon. It also means it's not even really black, it's just very dark grey. And that the event horizon isn't real. A black hole in this sense is just a very elaborate mirror. It makes sense to me that the object falling in will bounce off the "event horizon" and become time reversed and then come out.  This assumption seems classically consistent but might not be what actually happens. It is just easy to imaging time slowing down to 0 and then moving negative from the outside perspective. 
That brings me to my questions: Why do people say there is an inside to a black hole? What does the inside even mean when nothing from our universe actually gets there? If the hologram at the event horizon is all that is required to describe everything that ever went in, why does a singularity even have to exist? Is it sufficient to say a black hole is just a shell of spacetime where these effects happen and the event horizon is just a limited edge in our universe? And if true event horizons don't actually exist, and black holes don't really exist, why do people keep saying they do? Are pure singularity with a true event horizon thought to exist but not give off hawking radiation, how do physicist get around the problem of having hawking radiation and pure singularities? Isn't the singularity inside the black hole from the perspective of the object going in the same as the event horizon from the perspective of something outside as it is where from both perspectives the object will be at time infinity? Why do we even bother describing an object falling beyond an event horizon when nothing about that object beyond the event horizon can come back to our universe, which means it is untestable and physics requires testability. There must be a paradox there because for something to fall in and be described by physics, we must learn of what actually happens and we can't do that without breaking the event horizon anyways as no information can travel out. 
I have read the answers to this, this, this, this, this and many other Phys.SE questions in regards to black holes. As you can probably tell from the question, I am not a physicist so my understanding of this is limited and I have not formal studied anything to do with general relativity and the schwarzschild metric used to model a black hole with actual math. My understanding is limited to the parts without math and things that can be described in normal words. 
Although there is a lot of questions here, since all of this is very much related, the questions are all very much dependent on each other, I don't know how I would separate them into different questions without continuously referring back to this. Also questions regarding do black holes actually exist seems to all be closed as duplicate but no-one seems to give real answers.
 A: I appreciate your curiosity, but you are asking a question that needs math to even attempt an answer. That does not mean that an answer based on math is correct, but the more experiments we perform, such as the recent LIGO test on gravitational waves, the more confidence we have that the math and physics behind General Relativity  has again not been falsified, which is the way physics works.

Why do people say there is an inside to a black hole? What does the inside even mean when nothing from our universe actually gets there?

This is an example of what I mean when I say that only math gives us a guide to black holes. You make a statement that cannot be proven, but look at the examples we have of near black hole type objects, such as neutron stars.  Our problem is that we need to explain where this extra mass that  may have  otherwise formed a "normal" matter object, instead forms a black hole, so where does matter go "to", at infinite density?
Nobody knows for sure what happens infalling matter once it passes the event horizon, but we sure can't say that it stops at the edge, otherwise black holes would not grow larger, and our observations indicate that they do accrue matter over time.
A: Your questions are really not mostly about whether they can only be answered mathematically. They are conceptual questions where some can be answered mathematically (or in reality, more correctly, using mathematics to help us figure out the consequences of various things), one talks about a paradox that is in fact still considered a problem to be resolved, others are misconceptions, and some are still in research. 
But @Countto10 answered some of those well, and generally pointed to an important part of any possible answers: that observations and measurements have led us to be more and more convinced that that there are, and we've observed, black holes (BHs) (eg merging, but also in the centers of galaxies, and in star groups where other stars go around what can only be a BH), and objects that are just a little too light that otherwise would be BHs (neutron stars). That is important. We do theorizing, which is one way of saying drawing conclusions using logic and math, and physical intuition, of other facts or theory. General Relativity (GR) has had many tests validate its conclusions, so there's something there also. The scientific method, meaning practical conclusions from the evidence then points to BHs existing. 
Next, some paradoxes or issues of BHs. Yes, it's an unsolved problem as to what is inside. Classical GR says noThing, except the singularity. Observations says we don't know exactly, but we know that BHs have mass and angular momentum, and can have charge (that's not a problem, though it does not occur easily and we've not seen any with charge, or other types of charges, but we think we know why - charges will tend to balance out). Mass and angular momentum must come from something. GR doesn't care, it just says the objects have them, and when we see gravitational radiation from merging BHs through LIGO we see that the mass (and energy) and angular momentum obey the relationships that GR dictates - the BH thermodynamic equations that Hawking and others figured out, that also showed that they have entropy as well as temperature. To be entirely correct, Temperature and entropy really came from calculations done and theorems proved that included Quantum Field Theory in a highly curved spacetime outside near a BH. But it all was consistent. 
In addition, Hawking and others used math techniques from topology and differential geometry to show that under certain conditions, when something like a horizon forms on a body that's collapsing, it is inevitable that it form a singularity. So we do expect singularities inside horizons for well founded reason --  GR says it must (under certain pretty general conditions).
Then we have the non-important fact (from GR) that BH horizons make time go infinitely slow for an outside far off observer. It does not matter because they come infinitesimally close to forming horizons and have more matter accrete into the BHs (or the horizon, we don't care), in a very very short time, and so for all practical purposes horizons and BHs are real enough. You have to read and understand why this is so, it's non trivial and popular write ups always cause confusion and incorrect conceptions.
Finally, you have the quantum issue of information loss inside the BH, and do we ever get it back. The answer remains pending, and including the idea that the information is in the horizon and the holographic principle, it is still being investigated. But it does seem to have some truth, and most people think there is no information loss, just storage - but you'll find 20 different points of view from any 10 physicists. It does not mean there is no progress being made, and partial answers coming out. 
It is known that using Quantum Field Theory and basic principles with GR, the horizon will have some of these issues unresolved, but entropy on it and so on seem to be here to stay. What we still don't have is a way to answer the questions definitely because we still don't have a quantum theory of gravity. Whether that is some version of String Theory, or it leading to the holographic principle (the AdS/CFT correspondence), or some other theory of quantum gravity, we won't know till that's obtained and accepted. But we do know one possible set of answers: there are no singularities inside the BH, but rather some very dense quantum gravity structures which in some way is also related to the horizon degrees of freedom. 
You've asked some questions that if anybody can fully answer and evidence emerges of it, they will have a 'valid' (or some approximation) of a quantum gravity theory. 
Meanwhile we understand the practical meaning of what  (for observations and further theoretical developments) BHs are, and how do we observe them and research what we are not clear on. 
That's the scientific processs. 
I'd recommend you read the BH books by real physicists like Thorne, Hawking, and others, and also String Theory and the holographic principle. The latter is a hot topic now. 
