Experience from a couple of years ago ( a few times, for work, also in Shiraz. ) . no problem at all. Extremely friendly population. very safe, no crime . drawback : As a woman you have to wear a head scarf to cover at least half your hair. all the time . but not in private homes.
Not to do : try to shake hands with women , talk about religion , getting involved in political discussions in public.
Nuisance , you will be constantly reminded that the US are causing the hardship they endure because of the sanctions .
The vast majority of the educated people are against the regime. unfortunately for them they are the minority in numbers in the country .
Booze if you must : avail in Christians outlets and in private homes, no need to bring some with you.
How safe is flying over Iran territory?
In my time , it was very safe , ATC there is quite efficient and working well. Now , after the recent shot down , I do not know...The revolutionary guards are unpredictable , and they are a real problem in the country.