I have a plant (I don't know what kind of a plant is it) which used to be in the hallway of the building I live in. I didn't really take good care of it and most of the leaves dried up and fell off. A couple of weeks ago I brought it into my apartment where I took better care of it. The leaves started growing again very quickly. But they had white spots on. I didn't bother too much about the white spots until a couple of days ago when the leaves started drying up. The white spots are a discoloration of leaves, not a covering.
Does anyone know why are the leaves getting dry and why do they have white spots on them?
EDIT: There are also some small black dots visible on the leaves now (the dots can be easily removed from the surface), but I couldn't see whether they are bugs or not (not even with a magnifying glass). I have also added a picture of these black dots (the picture at the right).
Here are some pictures:
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