What is a Fact?

When relationships are simple, the word "fact" is used instead of "law".

I'm not sure I understand your sentence, so I will state what I think a fact is. A fact epistomologically speaking is that which is the case. It is not what I theorize is the case or believe is the case, although it may well be. It is not a construct-- a conceptualization from many facts-- that leads to a theory or a law based on an accumulation of evidence. The reason for this is the distinction between subjectivity-- images in our mind-- and what objectively is.
To make this clearer, I will state some facts and some non-facts. Now, non-facts do not necesserily equate to non-truth or nonsense. They are simply what is objectively real.

1. Every snowflake is unique. This is a non-fact. We have no way of establishing this obejectively. There are after all a lot of snowflakes.

2. Evolution is true. A non-fact. It is too sweeping a statement to reduce it to an objectively verifiable claim.

3. 2 + 2 = 4. A non-fact, as the symbols you see are expressions of deductive logic based on a prioris.

4. "If you died without a will, you would die intestate." Tautologies, essentially A = A, are not facts, as no meaning is added to the proposition. The indicative conditional phrasing however can be factual, i.e. "If X, then Y".

5. The speedometer of my car in the garage shows zero. This is a fact on in so far as we can trust the realities that statement implies, that there is a car, that there is a garage, that the speedometer is not broken, and so on. It is similar to this statement: "Washington is the capital of the United States", a fact so long as there is a objectively verifiable correspondence with the terms in question to the real world. This is really a compound fact as each term relies on whether or not it is the case, i.e. there is such a place as the United States, and so on.

The idea is to separate the "isness" of existence from the apprehension of existence by humans or instruments. This is no small task. Bertrand Russell uses an example where he looks a timetable and finds it is stated that a train leaves King's Cross for Edinburgh at 10 AM. A fact? Russell writes that "I shudder when I think of its complexity. If I were to develop the theme adequately, I should be occupied with nothing else till the end of the present volume, and then i should only touched the fringe of the subject.." He goes on to discuss the social aspect, the physical aspect, the definition of terms, the legal implications, the question of time, and so on. Russell associated datum with fact, and datum, he says, is something that we know without inference. But I'm not sure this is a good definition.