Docs, could a person have both sickle cell anaemia and thalassemia at the same time?

Yes: Both sickle cell and beta thalassemia affect the same gene; each person has 2 copies of that gene. If you have a sickle mutation on one gene and a thal mutation on the other you have sickle/beta-thal, which behaves much like sickle cell anemia. You can also inherit sickle cell anemia and Alpha thalassemia together.

Yes: Sickle cell anemia can be sickle trait or sickle cell disease. A patient can have an alpha or beta chain process which can be a source of alpha or beta thalassemia trait. The best way to verify is to do an hemoglobin electrophoresis, which will identify the type of hemoglobin the patient has. Check with your doctor.