DY,
1. The person who must signs that form is the plaintiff. Thus, if the wife is the one who files for divorce she is the one who must sign.
2. All it says is that the marriage was solemnized by a member of the clergy or the Society for Ethical Culture and that to the best of the signer’s knowledge all barriers to remarriage have been removed. How a secular court would interpret that in light of the Establishment and Free Exercise (f he goes OTD or she becomes a BT and he does not) clauses is a question mark. If it is considered a religious ceremony then it would seem that the same prohibition against required prayers in public schools would apply. It could well be that it will be interpreted to only mean that secular legal barriers have been removed.
Joseph, for the Chazon Ish’s words see http://www.hebrewbooks.org/pdfpager.aspx?req=14331&st=&pgnum=327
http://www.hebrewbooks.org/pdfpager.aspx?req=14331&st=&pgnum=327