1) Yes. The azimuth angle conceptually gives you an arrow along the ground which points towards the sun. The zenith/altitude angle tells you how far the sun is above the horizon. Together, the azimuth and zenith/altitude angles give you the information needed to point towards the sun in three dimensions.

2) Yes, but you need to understand that the zenith angle and altitude angle are two different ways to express the same thing - zenith angle is the angle down from vertical, and altitude angle is the angle up from horizontal.

3) Your English is a bit mangled but if I understand you correctly then yes, this is correct.

If you want to validate your calculated azimuth and zenith/altitude angle then do the calculation for the current time and position, and see whether the result correctly points to the sun.