As a Persian speaker, we do use "In fact" and "Actually" in the spoken and written language. And it is quite formal. I think when we want to add more details to something, or say something in another way (as it is in other words, however we have this phrase too), or to be more clear and factual and direct we use it.
But as I used it in some English sentences, I am told that is informal! OK, then what are the formal ways for it?.
For example these are some literal translation of the phrase usage in my language and I do feel a need for a formal equivalent phrase (for "in fact", and "actually") in English.
In this paper we do this…, In fact we simulate the way a human user do this.
We should help each other, in fact it is the sign of our humanity.
A pregnant woman shouldn't smoke, in fact, smoking pose hazards for the infant.
Best Answer
Your three examples look almost fine to me. I'll tell you first that "in fact" certainly doesn't sound informal to me. I have used and do use "in fact" in papers for class quite often to add exrta information of emphasis.
HOWEVER, the mistake that you're making here is that you're using commas. I don't think you'll ever find "in fact" not at the beginning of a sentence. There are rare instances where it can appear within a sentence, but usually, the use looks like this:
So, now to improve your three examples:
(Sidenotes for you on grammar: "smoking" is a single subject, so the verb should be conjugated as poses in the third example. "In fact" is basically always followed a comma.)