The fact is the country is changing in the Ramadan and making it more difficult for non-religious/non-muslims to pass the days (many Iranians don't fast and have difficulty in that period of the year).
Of course you'll find most shops open but probably many restaurants won't give service during the day. However some will still remain open for the people that are not fasting (due to several reasons: illness, travellers, ..) - as conclusion you'd be allowed to eat as long as you are not publicly advertising for it. That's the one thing that the religious observers won't stand and if they find you eating in the public probably they are going to warn you.
Overall I won't suggest Ramadan (specially in the summer period) to visit Iran, it will be a bit difficult but if you have to don't worry.. it has its own beauties, you will have many special foods (Ash, sweets, ..) and in the evenings you will find many people dining outside.. just keep in mind to not publicly shout you are eating and you are fine.