Is there a possibility that a single woman can have a cervical cancer even if she did not deliver a child?

Yes, cervical cancer is not really affected much by the lack of having children. Although having children is also a risk factor for cervical cancer and not having children is a risk factor for having ovarian cancer.
There are two strains of HPV that cause cervical cancer. Some people are very ignorant and think that all cervical cancer is related to the HPV virus. Those people are most likely one of the 85% of US citizens who have been in contact with some strain of the Human Pappilomous Virus at some point in their life, but like to take stabs at people for having Cervical Cancer. Another word to the wise is that HPV is sexually transmitted and condoms do not protect against the virus for it is a skin to skin contact so anyone is at risk of HPV if they have ever had sex!
At any rate back to cervical cancer. A virgin can get cervical cancer and many times this cancer goes left undertected because there are no early warning signs for it, which is why annual pap smears are of importance in detecting the abnormal cell changes that can cause cervical cancer. As well, pap smears are not 100% in diagnosing cervical cancer because sometimes the cancer is within the cervix and not only on the outer layer where they scrap a sample of cells from. At other times the cells which were collected were not abnormal cells because the practitioner did not collect the abnormal cells from the area that has cancer on it. Sometimes doctors shrug off symptoms as infections and Pelvic Inflammatory Disease and have misdiagnosed women who actually had cervical cancer. So, be very proactive with your health and keep going and getting second and third opinions if you believe there is something wrong with you. You may very well save your own life!

yes she can

Absolutely.

Yes, cervical cancer is caused by a sexually-transmitted virus, human papillomavirus (HPV).

yes it is possible. Has nothing to do with how many children you've had or not had.

yes by all means....