1) It seems likely that Iran is behind the recent attacks on ships in the gulf of Oman. I don't automatically believe US government propaganda, but from everything I read Iran is the probable culprit.
Iran is supplying the rebels in the Yemani civil war, SA is supplying the government. The rebels are increasingly using clever techniques to attack Saudi interests directly, but there is no reason to believe that the Iranians are directing those attacks even if you see Iranian arms any more than to believe that the US government is directing Saudi involvement because the Saudi's are using US weapons.
2) These attacks make sense. The US is putting pretty intense economic pressure on Iran. Iran needs to push back in order to force the US to give it a reasonable chance of negotiation. These attacks threaten US interests and the world economy. It is a clear message that the US can't continue its hard-line policy without paying a heavy price.
I think the opposite. They make sense from the perspective of the Houthi rebels who are generally incapable of striking back against the Saudis so will take what they can, but the Iranians win by making the US the bad guy and attacking a Japanese commercial vessel the same day that the Japanese Prime Minister was visiting Iran does the complete opposite of that. I also think that these attacks do extremely little to threaten the world economy and completely nothing to impact the US. They are a black eye to the Saudis, nothing more.
4) The cost of winning a war in Iran will be very high. If you doubt this, remember our experience in Iraq. There will be another drop in US prestige, severe unrest in the middle east and a bunch of expected and unexpected consequences from the inspiration of more terror groups to severe oil shortages.
You have barely captured the impact of a war against Iran. Iran has 3x the population as Iraq and serious allies in China and Russia. During the early days of the Iran/Iraq war when Iran was completely isolated and Iraq had the support of the world, Iran basically sent in waves of cannon fodder to push the Iraqis back. It would be a blood bath to invade Iran. The more likely scenario is US strikes against Iran, much like what we did in Bosnia. Still, you are right that we will not make friends and influence people. The Chinese in particular will not appreciate the threat to their oil supply.
7) If we don't want a war, the only other option is for the US to soften its negotiating stance with the idea that Iran would do the same.
Unfortunately, the US has no credibility. We made an agreement with Iran, Iran complied with their part of the agreement, the US unilaterally broke it then imposed harsher sanctions than were in place before the agreement. How does Iran and the international community proceed in the future especially given that the US administration is now being led by people who have said (for decades) that you can't negotiate with Iran? We are in a terrible position to negotiate our way out of this if we start it.
I don't know about anyone else, but I find this a little scary.