1) Correct - polishing does take a small amount of clear-coat away... also depends on the 'cut' or the harshness of the polish... i.e. some will take alot, some will take barely any.
The upside is, you really don't need to polish the car that often.
If you polish it properly the first time, and use a good sealant and wax, then realistically you don't really need to polish it again for a fair while (6 - 9 months odd? if you keep it well maintained, with regular washes and waxing etc)
2) wax forms a protective layer between the air and the paint - yes, wax whenever you feel like it (generally not needed more than about once a month (as a minimum) unless its left outside in really shitty conditions.
3) Clay has mild abrasives in it, and you can get different compounds of clay... some aren't so good, and can easily damage the surface of the paint. Yes, clay will take very minute amounts of clear away with it.