Answer: The easiest part of your question to answer is the last part. Those flying insects are probably fungus gnats and they are common pests of indoor plants. They feed and breed in moist potting soil so the best control is to provide a barrier between the top of the soil and the gnats. A layer of gravel or sand will keep them from the potting soil or you can use a soil drench such as Gnatrol or insecticidal soap.
In general, sago palms grow best in bright light indoors but not direct sunshine. Try moving your sago back away from the window or placing a sheer curtain on the window to block direct sunshine. The yellowing leaves can indicate overwatering (or sunburn) so try watering less frequently. Once your sago adjusts to its growing environment it should perk up and you can remove the old dead fronds.
Good luck with your sago!
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