First of all, gravity is not a fact; it is a theory. To be more precise, it is a fact (only in casual terms) that "on the surface of Earth in free air, if I drop something it will fall to the ground." (Note this statement is still not always true.) However, WHY this occurs is a theory. So by "gravity" here I am referring to this why -- the "theory of gravity."
Theories are abstract and conceptual, and they are never known to be correct or incorrect. Rather, we build a corpus of evidence for or against them -- we never know their validity 100% for sure. For example, at any point in the future, we may find some piece of evidence which disproves gravity as we know it. Then, we will be forced to revise our theory of gravitation (e.g. when general relativity was discovered).
A fact is something that is 100% true. If I say that "Sacramento is the capital city of California," then this is a fact because we defined it that way.
It could be that the theory of gravitation is 100% true and hence a fact. However, we will never know this, so to us it will always be a theory. Sometimes, people feel so sure about a theory that they go ahead and call it a "fact" or a "law" -- but this just indicates that a lot of evidence supports it and hopefully no evidence (yet) invalidates it; it is still a theory. (So to be precise, my original "fact" about dropping something is really a theory with LOTS of evidence!)
So to answer your question, a theory can be correct or incorrect. If it is correct, then it is also a fact. However, we will never know 100% whether it is correct, so to be precise we should continue to call it a theory.
A hypothesis is any testable, falsifiable conjecture. I can hypothesize that gravity is negative at one particular spot in your back garden.
As I understand it, a theory is any hypothesis that is believed to hold (at least for now, under the conditions it's thus far tested under, or based on the evidence we already have). In other words, a theory is a hypothesis that is provisionally considered true.
Thus, my hypothesis about your back garden could turn into a general theory of conditions under which gravity turned negative, if observations were made which supported it (which is, admittedly, unlikely!).
I'd agree with the Sacramento example above, i.e. that the only things we can consider facts are things that we've agreed upon/defined. This is a smaller set of things than people normally call facts.
Theories are abstract and conceptual, and they are never known to be correct or incorrect. Rather, we build a corpus of evidence for or against them -- we never know their validity 100% for sure. For example, at any point in the future, we may find some piece of evidence which disproves gravity as we know it. Then, we will be forced to revise our theory of gravitation (e.g. when general relativity was discovered).
A fact is something that is 100% true. If I say that "Sacramento is the capital city of California," then this is a fact because we defined it that way.
It could be that the theory of gravitation is 100% true and hence a fact. However, we will never know this, so to us it will always be a theory. Sometimes, people feel so sure about a theory that they go ahead and call it a "fact" or a "law" -- but this just indicates that a lot of evidence supports it and hopefully no evidence (yet) invalidates it; it is still a theory. (So to be precise, my original "fact" about dropping something is really a theory with LOTS of evidence!)
So to answer your question, a theory can be correct or incorrect. If it is correct, then it is also a fact. However, we will never know 100% whether it is correct, so to be precise we should continue to call it a theory.