Is it possible to have endometriosis without having had a child?

Yes. In fact, a significant number of women develop endometriosis at a young age, often ever before attempting to become pregnant. In fact the presence of endometriosis can make fertility more difficult.
Yes. Endometriosis is the implantation of tissue from the lining of the uterus outside of the uterus that can cause severe pain. Symptoms can present at any age after a woman starts menstruating, it may cause infertility.