Tehran has more potential leverage inasmuch as they've credibly demonstrated they can block the Strait. Whether they have more actual leverage than before is uncertain–trade flows are routing around them. And their own shores remain blockaded. (Just because the U.S. has less leverage than it did before doesn't mean Iran necessarily has more.)
"Shut down" is not particularly accurate. America and Europe can route around. The only ones fucked are the Gulf carriers.
What's to stop them? The enormous pile of ordnance floating in the gulf of oman that can be easily dropped on Tehran, for one...
Probably not. The other comment is right: cutting cables means having its own cables cut. (Tehran is also probably weighing whether it wants to continue mobilising almost all of its neighbors against itself. Trashing e.g. Kuwait for shits and giggles isn't strategically productive.)
Interesting point. It might be a good time for some good old-fashioned false-flag action.
It's always "a good time for some good old-fashioned false-flag action" if you can pull it off. Given Riyadh and Abu Dhabi are already bombing Iran, and are now unaligned, there wouldn't be much for the U.S. to gain from something like this. (And if Israel were to pull off a false-flag operation against the U.S. now isn't better or worse than tomorrow or yesterday.)
It took an idiot to try and actually use the full force of the USAF against Iran and reveal that the force was manageable- not great, but not going to topple the regime. And once that force was used and Iran's leaders realized it could be survived, that threat became much weaker, forcing a decision onto that previously mentioned idiot, he could either escalate to use greater force (some form of ground troops) or admit that he made a mistake and lost a war. And I suspect that the same will be true for Iran: the threat of cutting those cables is far more potent than the actual effects of cutting the cables.
The Internet is, it turns out, pretty good at routing around damage. The Russians have done some cable cutting in the Baltic Sea and it is annoying but it is not a winning move.
Or blocks repair ships after normal accidental damage?
It's information war to scare US companies away from the middle east.
This is the only fight they've been preparing for. They knew they were going to be facing an overwhelmingly superior navy and air force. That's why everything is dug in, buried and hidden. It's also why the propagandistic idea that they're a "terrorist state" is stupid, because a terrorist state would be prepared to do terrorist damage. The only terrorist arming and funding was from the US and Israel to people in Iran. I don't even see any heightened security at any level in the US - we're not even expecting anything.
Don't believe that the US can eradicate all ability for Iran to do something as trivial as cutting an undersea cable anytime soon. They would still have the ability cut the cables as a last gasp after they were totally defeated at every level.