Can you sue a church if your father died while volunteering?

I am very sorry for your family's loss. I would recommend investigating this matter thoroughly and developing possible theories of liability based upon the facts uncovered.  Do not delay reaching out, as witness statements and evidence need to be obtained and preserved etc.  There is a  2 year Statute of Limitation covering Wrongful Death lawsuits in Florida.  

Possibly. Who provided the ladder, your father or the church? Did you take pictures of the ladder? Does the ladder still exist for expert testing to see if it was defective in any way?. If the church was negligent by providing him with a ladder that was defective , then you may have a case. The issue is whther your dad was negligent for his damages or was the church negligent for his damages. Also the workmans comp laws may become an issue, but exploration into that issue would be required. Also, who are the surviving family members your dad left behind? The wrongful death act only allows certain family members to sue.  Discuss in private with counsel here in Florida.