That reasonable view is actually a classic philosophical position called 'naturalism'.
I'm hesitant to commit to categories, but I'd normally say I'm a materialist. Smart, with Armstrong agreeing, said materialism is the view that the only entities and processes that are real are those acknowledged by physics from time to time; and that seems about right.
Naturalism: that all things that exist and all events that happen are natural, operating according to the laws of nature (i.e. physics).
That accords pretty well.
Now, of course, this can quickly become a sort of a tautology (merely saying A = A) -- of course everything we see or that happens has to be natural. Right? How could it be otherwise? (see my point??)
The basis of my view is three assumptions. They're assumptions because in each case I can't demonstrate their correctness without first assuming they're already correct. They are:
That a world exists external to the self.
That the senses are capable of informing the self about that world.
That reason is a valid tool.
Fortunately for me, anyone who posts here demonstrates agreement with the first two, and fingers crossed, the third as well.
[External] reality is therefore the world external to the self, also called nature, the realm of the physical sciences, the sum of all things and processes that have objective existence, and so on.
Applying this to the point you make, yes, 'real' means 'shown to exist in nature / the world external to the self / the realm of the physical sciences.
I say 'shown to exist' because I use the correspondence definition of 'truth' ─ truth is a quality of statements, and a statement is true to the extent it corresponds with / accurately reflects [objective] reality. On this test the Higgs boson was not real until 2012; before that it was a hypothetical particle. Equally, in the latter 19th century the lumeniferous ether was real; and after Michelson-Morley it wasn't. The earth's crust was likewise solid and unitary until the development of modern tectonic theory starting around the 1950s. Dark matter and dark energy are not presently real. And so on.
'Common sense' is merely the accumulated life experience of a person, where they learn how nature, and people, and society work on a practical level.
I don't claim it as 'common sense'. I say (a) it's consistent with my assumptions and (b) I haven't yet met anyone who doesn't share at the least the first two of those assumptions.
Our 'common sense' tells us all (all 100% of us here and all other people that are sane) that nature operates pretty consistently, and is quite real.
No, the consensus of the best informed and sharpest is an essential part of science. Analogies to that are found throughout human affairs,
a question like:
"Where's the proof of the unnatural?
is a question that is...well...a tautological type of statement, really.
If X isn't known to exist in nature then the only place it can otherwise be known to exist is in an individual working brain that contains the concept of it, or imagines it. The concept of the Higgs boson is half a century older than the Higgs boson itself. (That's to say, the statement 'The Higgs boson is real' wasn't true till then. Truth is retrospective, not absolute.)
If an event was only natural then it'd be only natural.
No, there are a great many event which are internal to a brain. We've evolved to see the world in particular ways, one major part of which is seeing categories ─ the difference between 'this chair' (the particular) and 'a chair' (the category), for instance. A great deal of human thought uses such abstractions and generalizations ─ justice, love, indignation, history, car, burger, psychopathy, one, two, pi to the e+i, asteroid, doctor, medicine, life, on and on. The question is how they relate to reality ─ justice as the abstraction from distinct examples of fairness (for which we've evolved an instinctive feel), two from instantiations of twoness, remembering that each instantiation is actually brought about by a human judgment, the onlooker who says WHAT we'll count, and the FIELD in which we'll count it ─ how many beers left in the fridge?
If it is supernatural then it cannot be replicated or observed at will
The supernatural is by definition not natural, not real. Therefore the only thing it can be is conceptual / imaginary. If it's ever found in reality, at that point it will cease to be supernatural.
God is a being, that is, an agent with free will, and competent to chose whether or not to allow individuals to discover Him, according to His own choice and standards (just like you or me have standards of our own).
No, Got is a concept, an hypothesis, with no real counterpart ─ a very simple proposition that has remained unrefuted for thousands of years. That's why there have been thousands of different kinds of supernatural beings across those years, and why, since we find them in every culture, it's reasonable to suppose devising them is an evolved instinct of humans, probably as a support to tribal identity, that which makes the advantages of cooperation possible, along with having stories, customs, language and so on. (And perhaps also linked to explaining mysteries like what is thunder, why is drought, why does life appear to leave a person dying, and where does life then go?)