This spring I purchased an indoor tree and I think it is a ficus. It has recently, over the last month, lost many leaves, and does not look as good as before. It looks rather bald. Is there something wrong with it? Do I have to cut it back?
No, don't cut this one back,it'll ruin its structure, and anyway, they bleed like crazy if you cut them. The thing to remember about any Ficus is they're fussy - they absolutely hate a change in conditions, and in particular, a draught. Indoors, most will drop leaves when the seasons change, so in spring and again in autumn, and mostly because the heating has started up in autumn and then goes off at nights, or has been turned off when the weather warms up, and it may be you have more windows and doors open in spring. They don't really like direct sunlight, but will tolerate winter sunlight through a window, otherwise they need reasonably bright conditions.
Situate it where it gets the least amount of draught possible (not near a window you open regularly) but where it gets sufficient light, and well away from heat sources such as radiators and other electrical equipment which might generate heat (computer, etc). In other words, it needs a spot where there's the least change possible throughout the year in terms of warmth/cold/moving air. Water when the surface of the compost is just about dry to the touch, but not shrunken from the sides of the pot, and empty out any water in the tray at the bottom after 30 minutes, and again later if more collects.
If the leaf loss is not excessive, it might just be normal leaf drop - they do drop a leaf or three quite naturally over time, as they grow.