You can safely remove dead/brown branches, since the tree has aborted them and pulled out the nutrients/resources that it could. Typically, those gnats are a sign that the soil is waterlogged, so they're more of a symptom than a cause. If you can, put the tree in a freely-draining mix (like 5-1-1 or gritty, which you can find if you do a little searching), and if at all possible, give it more light.

-Tom

Thanks, Tom! I'll get my pruning shears out and snip off the dead bits, and look for a better draining soil. This tree was a gift, and the instructions that came with it were severly lacking in proper care info! (I think it was purchased from maybe QVC and shipped to me). I have it in a south facing window, and make sure to leave the blinds open all day, so I'm not sure if more light is possible. As for the gnats, I thought it was too dry (I water once a week, if that), but I'll try to back off on watering a little more.

Sorry for my ignorance, but when mixing up the 5-1-1 mix, is the lime and fertilizer necessary if my soil is miracle grow potting soil? Also, instead of pine fines, can I use like orchid potting soil (more bark-like)? I have orchids, so I have plenty of that!