1. In my opinion mid-spring for example in May is good time, because cities like Shiraz and Isfahan are very crowded in Summer and beginning of the Spring (Eid Nowruz) and many Iranian tourists visits these cities in Summer and beginning of the spring. 2. Depends to you, Are you going to travel to Shiraz with a tour? with airplane or with train or bus or your personal vehicle? Cost of a 3 days tour to Shiraz from Tehran with air travel and accommodation in a 5 star hotel is around 350,000 to 400,000 Tomans. 1 USD equals around 1750 Tomans in free market and 1226 Tomans in banks. So you can travel to Shiraz with less cost too.
the best time to go to shiraz weather-wise has just past. The airline tickets from tehran to shiraz 2 way is about 100-150$ or maybe even cheaper. If you know farsi you shouldnt have an issue, if you ask around people are nice enough to help you out, but if you dont know farsi you should only ask someone who you think can speak english, e.g. one who looks like a university student. you shouldn't have any problem with security as long as you avoid some neighborhoods and avoid picking on those who look like thugs.
If you're not an old man, I'd suggest you just travel to Iran and take it as it comes. Its not that difficult and people are very helpful. There really is no need to prepare years in advance. And truth be told people will show you extra consideration if you're not Iranian. I know old Swedish ladies who've travelled to Iran so you should manage.
3. I have a Russian passport but my brother has an American one. Will either of us have any trouble with Iranian authorities?
In all honesty, it sounds like a drug deal right there.
Of course planning is never a bad thing, I'm just saying that travelling in Iran is easier than most people think. The tourism infrastructure may not be as developed as other countries but that just ads to the trueness (is that a word?) of the experience. People tend to be kind to strangers and won't try to rip you off as soon as the opportunity presents itself. Due to its isolation, Iran is still pretty much unspoiled and genuine. Since your brother is an American citizen maybe you need to get that tour though, but otherwise I would have advised against it as it only limits you. Iranians may not be fluent in English but people know enough (at least the younger generations) to communicate with you. The Iranian culture is still much more similar to yours compared to, lest say, any Arab or East Asian one.
My friend you seem to be worrying too much, once you go to Iran your view will change completely.many Americans go to Iran, no body will do anything to you.those people who were arrested for spying were trying to spy by going into restricted building probably.just go there and have a great time.I want to visit persepolis too, visit there and come here with and tell us about your experience.
There was that one recent case though with American ex-Marine that was convicted of spying for the US while in Iran. He remains in their custody and might be executed. My question is: what did he do wrong that we shouldn't do?