I think its a variety of Colocasia, or Elephant Ear plant, and the pot it's in is way too small for it. These plants can get up to 9 feet in a season - they grow from a tuber, and are tropical, so in temperate regions, will be planted outside in the ground once all risk of frost is over. Given the pot is too small, its likely the symptoms you're seeing on the leaves are due to this, because there's no room for the roots to develop properly. You would need a much, much larger pot over time to enable its correct growth, but it isn't really a suitable subject for a balcony, unless the area of the balcony is very large. If you live in a tropical area, the plant won't die back in winter either.
Some information in the link below about these plants, though the one displayed in the picture is a particular variety with darker leaves - note also that Elephant Ear is a name also applied to Alocasia, a plant that's closely related and not dissimilar in growth habit.
http://landscaping.about.com/od/unusualplants1/p/elephant_ears.htm
With regard to the 'white powder', it sounds as if it had powdery mildew and this infection is often related to dryness at the roots of the plant - it wouldn't be difficult for the plant to get too dry given its in such a small pot. If it happens again, spray the leaves thoroughly, top and bottom with a solution of 1 part cow's milk to 9 parts water.