The analemma would stretch in the north-south dimension.

An analemma is an egg-shaped or figure-eight curve which results when the sun's position in the sky is plotted over the course of the year at the same hour of mean solar time every day.

Yes

If it is on a map or globe, then yes, it does.

No, an analemma is not limited to only north of the Tropic of Capricorn. An analemma is a figure-eight shape that represents the Sun's position in the sky at the same time each day throughout a year. It can be observed anywhere on Earth, as long as there are daily changes in the Sun's position relative to the observer.