Is it possible for 18 year olds to have stomach cancer?

Yes, but very rare. It is rare to have gastric cancer at such a young age. However, a familial type of gastric cancer does exist (hereditary diffuse gastric cancer). Worldwide, the incidence of stomach cancer among population aged between 25-35 is increasing suggesting perhaps there is a new enviromental exposure.
Unlikely, but yes. This is extremely rare, but there are genetic disorders where this happens.