The brown spots are hard to diagnose as they might be a minor leaf infection (fungal or bacterial) or a response to environmental stress (maybe low humidity, or being in the path of an HVAC vent, where cool air blows directly onto the leaf). Symptoms between the two can sometimes look similar to each other. There are few, if any, fungicide sprays labeled for use indoors, and they cannot cure existing infections anyway, so management usually revolves around prevention of more damage by keeping leaf surfaces dry (that is, not misting with water often), avoiding areas of low humidity, giving plants good light (close to a sunny window), and making sure watering is neither too frequent nor too infrequent. (Feel the soil a couple inches down and, when it becomes dry at that depth, water thoroughly. Make sure any water collected in a saucer under the pot is emptied so the drain holes don't soak that extra water back up, potentially drowning the lowermost roots in the pot.)

The white residue is a common insect pest called mealybug. They can be hard to eradicate if numerous, but mild infestations (as this appears to be) can be dealt with by wiping them off the leaf with a damp paper towel. If their numbers keep rebounding after removal, check the root ball by lifting the plant out of the pot; mealybugs sometimes infest roots as well, and when they do, can be difficult to control successfully. A systemic insecticide would be an option of last resort for both a heavy above-ground or root infestation, though such treatments can take a while to start working since the granules need to dissolve and have the chemical absorbed by the roots and moved up into the foliage. If used, be sure to follow all label directions carefully, and make sure the product is labeled for both mealybug control and for use in indoor settings.

Miri