"The man introduces himself as the father of the child."
Translation:Mannen presenterar sig som barnets far.
From what I understand, adding själv at the end adds another layer of direction, back to the man: The man introduces himself to himself as the father of the child. That's somewhat nonsensical, so compare the following two simple sentences:
han lär sig svenska: literally "he learns (him) Swedish", or he teaches himself Swedish.
han lär sig själv: he learns himself
Adding the själv at the end makes it introspective.
lik only means 'resembling' or 'similar', it's an adjective. Maybe you're thinking of lika, which can be used to translate as in the construction as … as, which is lika … som in Swedish.
(ok there's also a noun ett lik which means 'a corpse', but I hope you'll never need to use that).
Both med and i don't make sense.
The English translation of what you wrote is "The man presents himself as farther of the child".
If you used i that would mean "in", which would be weird.
Similarly, using med would mean "with" — which would mean he is the father with the child — and not necessarily that he was the father of the child.
It's largely archaic outside of terminology. Since this sounds like e.g. a medical or legal context, it could be used. But in everyday Swedish, not so much. The default is barnets far, since that's usually the much better choice. We mostly don't even accept fader/n in the course.
Haha, you should address this to Luis, the founder of Duo, since he has personally asked teams to accept both versions. :) Actually, we tend to use pappa more often in Swedish than you use dad or daddy in English, but there's also something regional about it, as far as I know, far is used more in Southern Sweden (I mean: without being more formal, as the more formal option it's used widely everywhere). – That said, generally father is more like far and dad more like pappa, that's absolutely correct.