Can a woman get pregnant after her husband has had a vasectomy, being the only guy that she has slept with?

Yes. A friend of mine had three sons AFTER her husband's vasectomy. The doctor asked if she was seeing any other men. When she answered she told the doc that she was and that they were all under nine years of age. DNA tests proved it. The husband had a very low sperm count so he was considered sterile, but the few getting through had amazingly good motility.