Is there a relationship between anklyosing spondylitis and pericarditis? what about chronic sinus inflammation and spondylositis?

Yes: There is an association between as and pericarditis. There is also an association with non-infectious lung fibrosis with cough and shortness of breath but i'm not aware any association with sinusitis - that may be another, separate plague to deal with - good luck.

Yes: Many immune related arthritis can lead to pericarditis and effusion. Can be taken care of by medical treatment.