Swans may or may not re-pair after losing their mate, especially if they were paired for a great length of time. However, their hormone levels will still rise during the mating/nesting season and they will still build nests or at least sit in an area until the hormone levels return to normal. Yes, the goose can see the swan as a pal and vice versa if they do not have a mate.

No, they will not mate or attempt to do so, but they will still hang around each other for company. Are there any other swans in the area? If so, it is possible that the swan may have mated without the mate sitting near the nest with her (if it is a female). Males will also build nests and sit until their hormone levels return to normal.

Once the swan (if eggs are laid and obviously not fertile if there is not a male swan) realizes that the eggs are not viable, they will leave the nest and eggs and return to their normal habits. The Regal Swan