Are you sure they are insects? There are many mites that fit that description. Are they rounded at the rear? If so ... could be mites.

Some mites are bad for plants, some aren't. I have lots of little mites like that in my worm composting bin, and the types in there are supposed to be harmless to live plants. I think they would only survive in your plant's pot if the potting mix included lots of nutrient-rich organic matter - compost and the like. Also, I suspect that they would be discouraged if the potting medium were dry much of the time. Do you allow the soil to dry pretty thoroughly before watering?

The dry brown edges do sound typical for what some begonias do in humidity that is too low for them.

some one told me it could be fungus gnats (brown, tiny, skinny looking insects that crawl or fly around the soil) and their larvae (white or clear, look like tiny worms). The worms looked like white thread, short and very tiny. Anyway it had about 3 leaves left. I repotted with fresh soil and the next day only one leaf was standing. The others drooped. Do you think it will get back in shape? I hope so, becasue it's one of my favorite.

it's typical for a begonia's larger leaves to droop and die when repotting. with luck and attention, it should come back if the rhizome is healthy.

-ming