How inflation creates a universe from nothing? I have a basic, mostly purely conceptual understanding of Quantum Field Theory, and after lots of Youtube (thanks PBS Spacetime!) I have an idea of how inflation works to turn the vacuum into a universe. Please correct me if I'm wrong.
There are quantum fields present everywhere in the universe at once. Excitations on those fields, caused by energy, are the vibrations that we perceive as particles
A field at its lowest possible energy state still has quantum fluctuations since, due to the laws of Quantum Mechanics, it is impossible for the field to have precisely zero energy. These quantum fluctuations are small vibrations in the field that usually quickly form and cancel each other out, and they can be thoight of as (although this is mostly to aid in visualization, since they don't have the exact same properties) 'virtual particles' popping in and out of existence.
At the event horizon of a black hole, some of the vibrations are 'cut off' because of the one-way boundary that is the evnt horizon, so the vibrations that would be cancelled out by these don't, so they are perceived as 'real particles', what we call Hawking Radiation.
So my understanding is this. An early universe is in the vacuum state, with only quantum fluctuations permeating the cosmos. The process of inflation causes points that were previously very close to suddenly become extremely far apart, going from a distance in the quantum scale of things to lightyears apart in a tiny fraction of a second. Since points of the quantum field which were very close together are suddenly way too far away to communicate, this effectively 'cuts off' the vibrations in one spot from the rest of the universe, turning those quantum fluctuations into 'real particles'
Is this correct?
 A: I think it is not possible to give a clear "yes or no" answer to your question, because it is a question about a research area where there remain many models which do not agree with one another, and we simply don't know which if any are right. The research area being inflation theory. 
Inflation or something like it may have happened, or it may not have happened. The biggest unknowns here are to do with entropy. Attempts to model the early universe in detail typically evoke (without always realising that they have done so) extremely special states of affairs. This makes it hard to assess whether or not a given theory has not so much explained something as shown that it would be the outcome of something even more inexplicable. Inflation does not escape this problem.
I think the main message here is that something rather odd is happening in our day in the interaction between research science and the wider public. The distinction between carefully constructed and tested ideas and mere speculation is blurred in many popular books, and You Tube channels are even worse. In elementary particle physics, progress over the last 80 years has required a partnership between experiment and theory. There are occasional examples where theoretical understanding put in place something well out of the range of experiment but which proved to be correct (Higgs mechanism being a good example). But there are also many examples of cases where experiments yielded surprises. Inflation is an attempt to grapple with physics at the energy scale $\ge 10^{15}$ GeV. Experiments have accessed up to $10^4$ GeV.
I think the best way to respond to your question is to encourage continuing interest in these areas, but also to encourage a greater role for the attitude "well we really don't know yet".
But one thing we do know is that every scientific model ever put forward for anything has invoked a continuity between one thing and another, between a prior situation and a consequent situation. The idea that physics suggests that something could come from nothing is simply a misdirection, a deliberate miss-use of words, presumably in an effort to gain readers or something like that. I mention this simply because the title of your question suggests that you may have been miss-directed into this sort of juggling with the meanings of words.
Among the authors well-placed to comment here, and who does a reasonably balanced job I think, is Sean Carroll.
Added edit to answer specific point at the end of the question.
Either with or without inflation, space is reckoned to have started from an early state presumably described by quantum gravity, and it grew extremely fast at early times. This resulted in energy density fluctuations being present on pretty much all distance scales. This is modeled theoretically by using quantum theory to provide a value for the standard deviation of the distribution, and then subsequently treating that distribution as a classical field having fluctuations over space and time with the given standard deviation. The move here from quantum to classical is rather glossed-over in the research literature; it is connected to the subtleties involved in the process called symmetry-breaking. 
(What is spontaneous symmetry breaking in QUANTUM systems?)
Anyway the main point for your question is that this is not like Hawking radiation. The fluctuations are already reckoned to be classical, or are treated as classical, whether or not there was a subsequent inflation to stretch them out. (I don't work directly in this research area; I got the above information from a book by Hobson, Efstathiou and Lasenby, and from various review and other papers).   
A: It was the Big Bang which created the universe, and the "nothing" from which it was created was most likely the fireball of a previous universe whitch collapsed into a Big Crunch followed by a Big Bounce. This is not the prevailing theory at the moment, though it hasn't been completely discarded. One-off Big Bangs which have no apparent cause and literally create a universe out of nothing and eventually dissipate into the dark nothingness of space raise all sorts of problems from the point of view of logic, which are avoided by a Big Crunch. Theories come and go and so does the evidence on which they are founded, so perhaps the Big Crunch will come back into favour some day.
I am very sceptical about the inflation scenario, and think we should await more evidence on this. Likewise with virtual particles, as there is good evidence to cast doubt on them. The Cassimir effect, for example, can be explained by more mundane mechanisms. The 40 orders of magnitude discrepancy between the vacuum energy required by QM and the cosmological observations with which it conflicts does not inspire confidence in the virtual particle theory.
A: Theories of inflation are not the same as universe-from-nothing theories.
There was already “something” when inflation started. In inflation, the universe (both spacetime and quanta in that spacetime) already existed, but it then became exponentially larger due to the energy and pressure of a theorized scalar “inflaton” field that would be somewhat similar to a Higgs field.
In universe-from-nothing theories, the universe emerges from a no-spacetime-and-no-quanta state, perhaps via quantum tunneling.
If what you meant was “How is inflation able to create so much matter and radiation?”, then there are two possible answers. The first is that energy conservation may not apply to the universe as a whole. The second is that, if it does apply, it holds because the gravitational potential energy of all that new matter and radiation is negative (just like the gravitational potential energy of the earth and the Sun is negative) and it balances all the positive energy of the created matter and radiation.
