Please tell me if I am correct?
Question: Have you ever been hospitalized or did you have serious illiness in the past three years?
There are two parts here, (1). Have you ever been hospitalized in your life time up to this point? (2). Did you have a serious illness with or without a hospitalization wihin the last three years?
If they were interested in knowing only the last three years, the question should be rephrased as:
Were you hospitalized or did you have a serious illness in the past three years?
You are correct. The question is in two parts. The first part asks if "you" have ever (at any time) been hospitalized. The second part asks if "you" have had a serious illness within the last three years.