I swallowed a dime, and I am wondering can I get esophageal cancer?

No. Limited short term coinage exposure and dime consumption have not been demonstrated to be independent risk factors. It is important you speak with your primary care / family physician. He/she can further assess your health and provide more individualized care and guidance. http://goo.gl/itxx2.
No relation . But see a primary care provider.
No. But if you keep swallowing things that are not meant to be swallowed you run the risk of injuring your esophagus or stomach and put your health at great risk!