We've been there in July and August and have had no issues with bugs or flies. We do have a canopy we put over the picnic table, but don't even put the screens on it.
Road noise is not an issue, it's back enough from the road ( unless you are up by the office-club house) that noise isn't an issue.
Airplane noise will very. There are a couple tour operations that have small single engine planes for tours of the area. Holidays and weekends are usually pretty busy, but I don't find it annoying. Generally, it's later in the morning before they start and they wrap it up prior to sunset.
You also will get a few private jets coming and going, but again, not a big deal.
Yes, we are still in Apollo Beach, but have been in the Keys since mid-December.