So the other day I was at a friends airstrip and another friend of his flew his plane back from it's annual inspection for him was that a commercial flight?
Yes. Happens all the time, unlikely he'll get caught or anything will come of it, but if he had crashed on the way home, and the owner said in the NTSB interview, "he was flying it back from annual for me" it would have been a problem.
Someone I know may or may not have flown a plane that he had rented on many occasions to an airport to get the radio fixed for the owner and didn't pay for the flight and got a little over 2 hours in the log book was that compensation?
Yes, same as above, assuming they were a private pilot. Again, outrageously unlikely that anything would come of it, but I wouldn't go filing an insurance claim if something happened.
If a parent owns a plane and lets his pilot kid fly it at no charge is there an issue?
No; that's the whole point. The issue would only come up if the pilot kid was acting as PIC for the parents in return for the free time. "Kid, I'm proud that you're a pilot; fly my airplane for free" is fine. "Kid, how convenient it is that you're a pilot. My medical just expired and I'm flying as a sport pilot, but I want to get a nighttime $100 hamburger. Fly me there and you can use the plane for free" is more sketchy. On the other hand, the gov't is pretty unrestrictive about gifts among immediate family members, so there are a lot more loopholes available in that case.
A strict interpretation of what is in that letter would be that an FBO, for whatever reason, that is operating at *any* loss on their aircraft rentals is causing the private pilots to be in violation of the not-for-compensation rule.
Again, only if the private pilot is acting as PIC in a way that directly benefits the FBO. The FBO is free to give away plane time. The pilot is not free to accept free plane time in return for acting as PIC
for the FBO (flying to maintenance, etc.)
Think of it this way: if the FBO says "you can fly the plane for free today," you can say "yes." If the FBO says "you can fly the plane for free today as long as you fly it to XYZ or carry XYZ with you," then you have to say "no."
What about aircraft clubs who let members fly planes, for free, to or from maintenance? The pilot is performing a flying service for the club, and being compensated for that.
I was under the impression there were various weird things you could get away with more easily if the pilot actually owned part of the plane (eg in a fractional ownership club), but I haven't read that part of the FARs recently enough to comment.
Dear Chief Council, I am a private pilot. A buddy of mine let me fly his 172, free of charge, for my wife and I to go on vacation. During the trip, I found 37 cents in change in the seat cushion and kept it. Did I improperly accept compensation for this flight?
No. Your buddy didn't benefit in any way from you going on vacation, so it doesn't matter that he let you use the plane for free, or that you took your wife, or that you found 37 cents. If your buddy works with your wife and said "dear god this woman drives me nuts, just fly her out of town for a while. Hell, take my plane and any change you find in it," then it's a problem.