Is there a possible relation between a chronic dental infection and sinusitis?

Possibly. If the tooth in question is a posterior maxillary (upper) tooth that has roots that are in close proximity to the floor of the sinus then there might be a relationship.
Absolutely. Absolutely there is a relation... Unfortunately these are tough to clear. Bottom line: the sinus infection will not clear until and unless the dental infection is clear. You may require surgey on the maxillary sinus to help clear the infection.
Yes. If the infection is draining into the sinus or is close to the sinus then it is very likely. Treat the dental infection immediately!