1) What does the Shariat say about the kids of the first husband? if the girl has a second marriage are the kids mehram or namehram to the second husband?

2) If the second marriage takes place the husband can take the kids as mehram and participate in their upbringing?

1) If you mean her kids from her previous husband, then, yes they are mahram for the second once he have the first sexual relation with her.

2) Yes