We don't, as far as I could see, know what the OP dislikes (the noise, perceived danger in case of forced landing, spying, etc.) about this. And we don't know if it really is the same plane or not. He does claim he doesn't want to cause trouble but just talk to the pilot (if it is one pilot). I'm not sure, but isn't it kind of strange of it really is only one airplane doing this?
When I started flying lessons, I also noticed how the noise is way less than one would think, and as you say, short duration. Leaf blowers are way more annoying, and last for hours. As do many things.
At our airport we have rules also for noise reduction, that we follow. We also are not allowed touch and go, unfortunately.
But all that said, some of the aggressive, condescending, put downs for someone asking pilots a reasonable question seem counter productive. Some helpful responses here too, to which the op showed gratitude.
To me the bottom line, small airports are in the endangered species list. I'm living in Norway now, (it's worse here...airport closings, plans for moving out to the country get met with mayors of small towns seeing no upside, if just a few constituents make trouble, plans get dashed.) but my father worked for some years for the AOPA in the Midwest, and almost all of his time was spent trying to keep small airports from being closed. Trying to get new ones,
The main point, it doesn't seem smart to go into attack mode, or correct. Confrontation will harden hearts that otherwise might be amenable. Some people of course are just against all airports near them, and yet it isn't helpful to assume anyone that asks is looking to make trouble and start a campaign to complain.
Don't we need all the good will we can get?