To address your concerns:
1.) Even when/if Iran gets the nuke, it isn't clear if they'll have a launch platform capable of reaching the US. Their main target actually is not us, and not Israel, but more likely their Sunni Arab rivals. Even so, their potential nuclear threat to the region is very serious and very real.
2.) I don't think this scenario is quite as likely. Russia already had its fun with Georgia, and I don't think we will see a repeat of this.
3.) This is considerably more likely than I think many people realize. Their long term agenda is to re-establish a sino-centric system of dominance over their neighbors, and now we're seeing this in their bullying of their neighbors in the South China Sea. In fact the situation with the Phillipines is most instructive, the only reasons that hasn't already escalated into a shooting war is because we have a mutual defense treaty with the Phillipines and an overwhelmingly powerful military machine that can enforce it. But this situation will not hold. It's an unfortunate tendency for them to overplay their hand whenever they think they have an advantage, no matter how short term, fleeting or nonexistent it might be. When they think we are too weak, whether it be in means, in will or both, they will test our treaty obligations and then things will get interesting.
4.) These guys came very close to a shooting war a couple of times since Pakistan developed it's nukes. The potential is there for sure, just for the traditional reasons. Now add to that China. In the context of a broader war with China, we could potentially see them go to war with each other again. Also in light of Pakistan's continueing instability, it's possible for Islamic radicals to eventually sieze power and decide to have that "final showdown", this is an area to be concerned over for sure.
5.) Fortunately unlike Pakistan our military isn't riddled with end of days whackjobs and has much better control over our arsenal, as well as more sane people with their fingers on the button.
So in short, you are right to be concerned about several of these. The next 10 years will be quite interesting indeed.