Can colonists be relocated during the Mayor phase?
All your colonists can be moved each mayor phase, including ones acquired during earlier turns.

From the rules:


  A player may place his new colonist(s), together with all the colonists he acquired from earlier rounds, on any empty circles on the tiles on his player board. Thus, a player may move a colonist placed on a circle or San Juan in an earlier round.


Since it is the last thing a player does during their turn, the first opportunity to remind them is after a new role card is selected or the Governor placard is moved (since otherwise it would still be during their turn.). It seems silly to place only the minimum number of colonists in the ship if "forgotten" at this point, and I can see how this could be exploited by players to not end the game as soon as it normally would. (Note: This rules seems is probably for later turns after a Builder phase has been selected and people cannot remember which new buildings have been built, and therefore how many colonists are supposed to be on the ship.)


  As his last duty, the mayor puts new colonists on the colonist ship to be used in the next mayor phase. [...] - If a mayor forgets (players may remind him) to place new colonists on the colonist ship, players later place the minimum (number of players) on the colonist ship.