Will Iran nukes cause an arms race? History says not likely and current nuclear programs in the Middle East say the same.
Will Iran hand off nukes to terrorists? Well, they have aided terrorists in the past (172), but they haven't given terrorists chemical weapons and they don't want their country to be flattened. Iran knows which lines will get it destroyed if crossed, so it avoids them and it will likely continue to do so.
Will Iran strike Israel first? Well, considering that a first strike will get it flattened, then no for the reasons stated above. There's also the fact that even it's rhetoric has primarily focused on "second strikes" rather than "first strikes" including the one in the OP.
That's what I said earlier about credible threats. Heads of state having been making threats since they have existed. It's the responsibility of a government to determine when those threats are credible and it's in the interest of the public to educate themselves lest the state mislead them in order to enter an unnecessary war.I would not doubt if Iran has bad intentions against Israel at all. They say they will do it if they have opportunity. Who are we to doubt the words out of their own mouths?