I'm thinking of privately asking my friend about the paternity of her children
Why would that even come up?
While being drunk, she might have talked about her past infidelity.
You should stay out of other peoples relationships. If he cheated she would still have his baby, he might have a love child. You could destroy a marriage.
It's the internet, it's all a game and no one knows you.
I might not know you or your friend, but in general it is not good to meddle in other people's business. I agree that your friend's husband should know whether the children he is raising are his own, but it should be your friend that tells him, not you.