How come Karin has a child with Sasuke (the guy she is obsessed with for so long) and than gives it to another girl to be it's mother ..
It is never stated that Karin is Sarada's mother in fact Kishimoto said in an interview Sakura is Sarada's mother. However, this may not mean biological mother, as Naruto had always explored and asked questions about the values of blood, lineage, family, and parentage. In garden especially, Sasuke never being around, Sakura and shin's conversation, etc. Gaiden is shown through Sarada, and it is shown she suspects Karin to be her um for shown reasons. Interesting to note how she talks about Sakura at the end of last chapter, again the questions on the value parentage. Also interesting to note there wasn't a single reference to love last chapter. So yeah either Karin or sakura the mum. Outwardly said to be karin most likely sakura with Karin having some possible connection judging by hints in garden and kishi's style. But ur the audience, u decide what u think and kishi will soon reveal the answers.