I don't think Ben is Alex's biological dad.
I do wonder about the day he was caught in a net by Danielle though, I always thought it was a bit fishy (no pun intended

) because he is soooooo important to the others yet he was the one that went to suss out the losties. This may have been his own choice but still a risky one with 'leader'. I believe Danielle has had some sort of contact with the others in the past - she said she had never
seen them but she had heard the whispers - maybe she struck a deal with Ben that day, maybe she would get Alex back if Ben was saved and so helped him to get closer to them, and get Ben his spinal surgeon. I think everything Danielle said to the losties up to that point was genuine.
I also wonder if Alex has ever seen Danielle, she has been on the island before and she had a boat so could go back whenever she wanted. She seems quite normal too so if she saw someone else on the island maybe she would try to speak to them - if she wanted to.
I'm still pondering on Carl - I don't think he is Alex's brother because Danielle would remember having another baby and I think if he was Ben's son (ciurtesy of Juliettes magic potion) Ben would care about him a bit more - I'll have to think about Carl a bit more...