An odd situation has arisen. The Americain player researched Agriculture and expanded his Capitol towards his previously played Great Person.

Should the American still be retain 1t for that Humanitarian's coin?

Normally one receieves the coin as soon as the tech (Metal Casting) or the Metropolis expands (ex. Greeks & Germans). Should the reverse hold true as well? Metropolis expands, return Person to the American sheet, loose out on benefits of said coin?

A coin printed on a great person is only valid if the great person is on the map. So if the metropolis was built over the great person, than the coin is immediately lost. However, the player keeps the great person and can place them back on the map at the start of the next turn and get the coin back. However, the hammer that would have been saved by that coin is lost for that short amount of time before the great person is added back to the map.

Yes, if the Great Person gets kicked off the board, then the coin is lost until he is re-placed on the map.