Learn English – Formal way of asking “Don’t we need to?”

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:

Running is very good for your health. In fact, 9 out of 10 doctors in the US recommend running daily to improve your health.

So, now to improve your three examples:

In this paper we do this.... In fact**,** we simulate the way a human user do this.

We should help each other**.** In fact, this is the sign of our humanity.

A pregnant woman shouldn't smoke**.** In fact, smoking pose***s*** hazards for the infant.

(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.)

In English, if we ask somebody to do something beyond one's authority to do so, one might say:

I know this is above my pay grade, but would you mind taking those cups back to the kitchen and not leaving them for me?

I knew I was going out on a limb in asking him to do it.

I know I probably shouldn't have asked him, but, the mess got to me.