Can a person who is paralyzed from the chest down still have sex or have children?

Sort of, and yes. Paraplegics have little or no sensation during sexual activity. Both men and women can have leg spasms, which make body positioning challenging. Men usually no longer have any or adequate erections. Fertility in paraplegic women is not changed. With a paraplegic man, there are special ways to collect sperm, which doctors can then put into his wife to create a pregnancy.
Yes. You can have sex and as long as there is vaginal stimulation, you will maintain an erection (like a spasm). However, you will not be able to ejaculate so you have to arrange for collection of sperm and use that sperm to artificially inseminate your woman. Some women prefers somebody paralyzed since the erection lasts as long as the stimulation occurs, allowing for multiple organsms for the woman.