If I had an abnormal pap with severe dysplasia level 3, does it mean that I have cervical cancer?

Not necessarily. This is an old term that correlates with what is now known as cin3 (or cervical intraepithelial neoplasia, grade 3), which is not technically cervical cancer but rather a precursor. Some can spontaneously regress, but some can progress to frank cancer. As such, treatment options can include anything from doing nothing to actually removing the offending lesion(s).
Possibly. The more advanced the dysplasia (abnormal cells) the greater the possibility of finding cancer in your cervix. The next stage of your evaluation is to obtain a colposcopy with biopsies. These 3-dimensional pathology specimens will then be evaluated to see if the disease has progressed to actual cancer. The good news is in most cases it takes 10-15 years from onset of dysplasia to become cancer.
No. You probably have cervical intraepithelial neoplasia 3 (cin3) which is a precursor to cervical cancer. Cin3 means the cells in your cervix are growing abnormally in greater than two-thirds the thickness of the mucus membrane of the cervix. If it is untreated, the estimated risk of progressing to cervical cancer is 12-40%.
Close. Severe dysplasia is the diagnosis for tissue that is markedly abnormal, but with still some features of normal tissue evident on biopsy - some cells would have some degree of normalcy. A cancer would have no normal tissue development apparent on the biopsy - all of the cells would be abnormal.
No. The pap smear is just a screening device that samples cells from a scraping. A more precise diagnosis requires a colposcopy and biopsy to look at a piece of tissue under the microscope. Severe dysplasia is a precancer, though if the pap shows severe dysplasia, there is a chance of invasive cancer so further evaluation is important.