Does a cat scan see almost every medical condition with or without dye injection?

No. There are many illnesses and problems for which ct is helpful. Ultimately, it is most important for the information obtained from the ct to be combined with the information the doctor obtains from examining you.
No. A ct scan does not see almost every medical condition, even with contrast. This is particularly of the brain, where MRI is more superior. In the abdomen, MRI (as in mrcp) is more superior for the bile ducts. Also not all ct scan are the same. Ct angiograms are done differently from other ct techniques. The uterus and sometime ovaries are also better seen on us or mri.