I could answer most of your questions with this: physics describes EVERYTHING. It is the study of the natural world.
But here goes:
How does physics serve to improve our understanding of physical systems?
Because physics tells us exactly what happens in these systems, it's more than just equations. Behind it all, physics can teach you everything you need to know about the system in question.
How do the principles of physics effect your daily life?
The most basic physical principles deal with particles and atoms and energy.... that's pretty much everything in the known universe... so I think that accounts for ALL the events in your life. People underestimate how basic physics really is. All other sciences are built off of it, ALL of chemistry is encompassed in physics, even biology (just at a higher level).
Describe something in nature that has become more compelling because of an understanding of physics principles
Describe something that HASN'T become more compelling! lol j/k. seriously though this is an opinion question. I guess I would just say space and time in general.
Is it possible to describe the whole natural world (chemical and biological) with a small number of physical principles? If so, how?
Oops, I already answered this

Yes it is possible, because as I have said, everything is made from matter and energy, and physics is the only real tool we have to understanding these things at the most basic level. Everything else (from the neurons in your brain) to trees animals, it's all built off of these basic principles.
Is physics a redundant science? Do we now have a clear understanding of the interactions between matter and energy on all scales? Is technological application the main thrust of physics research today?
Hell no. I for one (and probably all physicists) will never stop developing our current understanding of the universe until I can stand back and say with absolute certainty that I know exactly how the universe works. There is a famous quote by richard feynman "Physics is like sex: sure, it may give some practical results, but that's not why we do it" What I'm trying to say is... i guess that ordinary people might only care about the applications of science research. But the scientists/physicists themselves care about the principles.
and no we don't have a "clear understanding" of the interactions between matter and energy on all scales. In fact I would say that we have a poor "understanding". Although we do have some fairly excellent ways to describe mathematically and predict WHAT will happen, we don't understand very well HOW it happens.