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The care of these trees is very simple. This link will take you to our articles on Norfolk Pines, where you will find all of the information that you need to grow these successfully: https://www.gardeningknowhow.com/houseplants/norfolk-pine/

This can have many, many causes. The most likely is that the area lacks the proper humidity, but there could be multiple issues. If this is only happening in one spot or two then this will be no cause for concern. If it is widespread, then you will want to start running through the checklist. This article will help you find out what is causing this: https://www.gardeningknowhow.com/houseplants/norfolk-pine/norfolk-dropping-branches.htm

Norfolk Pine cannot survive temperatures below 35 degrees F. You can wrap the pot and plant with an insulation blanket, but if your temperatures dip down it could harm or kill the plant.

Best of Luck.

Norfolk pines require high indoor humidity which is difficult to achieve during months that the furnace is on. Misting is only a temporary measure so the key is to find a place that gets sufficient light and humidity. Clustering indoor plants together may help as well as setting the plant over a tray of water with pebbles in the tray. You don't want the plant itself to sit in water as too much water causes browning of needles. So does too little water! I think this plant needs a larger pot and careful watering. There must be a drainage hole in the pot. I would not prune because it isn't certain the entire branch is dead. Needle drop may be followed by new needles. (This isn't a true pine tree.) Two articles to help you along: https://www.gardeningknowhow.com/houseplants/norfolk-pine/norfolk-island-pine-care.htm
https://www.pennington.com/resources/fertilizer/indoor-gardening/nurturing-norfolk-island-pines-year-round

It will recover, but it will not retain its original shape. Pruning some of the dead growth off when it warms up will help it out some. Here is a collection of articles that will help: https://www.gardeningknowhow.com/houseplants/norfolk-pine/

These sound like fungus gnats. They are not harmful, and in fact, can be beneficial to the soil. They will really only come out when the soil remains too wet for too long.

I would make sure that the soil dries out pretty good between waterings to prevent these from being overbearing. They do contribute to healthy soil, but they can be a problem when the soil is too wet.

If you still want to get rid of them... Rosemary oil in warm water left to cool then watered in on the next watering will rid the soil of these. Just be aware that I do not recommend totally ridding the plant of them. They do help the soil out quite a bit.