What is the solution when a patient swallows the silver amalgam fillings while applying it? what happens to him? are there medications that can be prescribed? and does it have an impact on his future?

No worries: And swallowed materials will pass without harm.

Not a problem: The mercury in the amalgam filling material is bound to the silver. The filling material will pass through your gastro-intestinal tract without incident. No special medications are required. No social procedures are required. As they say, "Everything will work out OK in the end."