Are cancer survival rates truly improving, or is it mostly due to earlier diagnoses making it look that way?

Both. Some cancers can be treated effectively and even cured, e.g., hodgkin disease, some tumors and leukemias in children. For others, e.g., prostate cancer it may be that it looks that way due to earlier diagnosis. Early diagnosis in cervical cancer, especially pre-canceous lesions has improved survival.
Both. Cancer survival rates are improving due to early diagnosis as well as better treatment.
Yes. They are improving gradually, mainly due to better treatments as well as earlier diagnosis. For most cancers, earlier stage means higher chance for cure.