That's up to you.
Depends on what result you want to achieve.
Yes.
What you've described is a violation of
section 50 of the New York Civil Rights Law. The logical thing to do is to contact whomever owns the web site in question and demand whatever it is that you want. Take down the picture? Money? Both? Something else? You can get a lawyer involved now to make the demand for you or you can do it yourself and only involve a lawyer if you do not get what you want.
By the way, and just to be clear, are you and your child's other parent on the same page with respect to this issue? For example, your post doesn't rule out the possibility that you and the other parent are not together and that the other parent consented to this use. Just trying to make sure we have all of the relevant facts.