Fool, you obviously have a distrust of sound engineers. Remember that it has to be a team thing with SEs and performers. SEs want to know what you want to sound like. True SEs are part of the performance. But if you become too prissy we tend to switch off.
A sound check should last no more that 30 minutes - maybe more for larger groups (the SE will have already been there for some time setting up the PA and EQing the room).
A frequency analyzer is a mere tool. You have to know what it is telling you to use it properly. What a good analyser will do is analyze "white" or "pink" noise to tell you what each room's natural sound frequencies are. This helps to balance the mains to the room (and avoid feedback) before the SE even tries to get the performer's sound down.
SEs have to listen to the performance. If you suck musically or play out of tune, the SE cannot fix that. The SE can make you sound the best you can. Most good SEs I know are very patient and slow to anger but if you really piss the SE off he can also make you sound like a real amateur. Remember that!
The remainder of your post was not relevant to sound engineering.