Unfortunately Iran's leadership is in a bit of distress and communication disrupted, and "involved in the conflict" is a very broad term - so they do make some effort to get chinese oil out, but any ship not asking for explicit permission from Iran - will have some great risk of being targeted.
Remember, the strait is not Iranian property, but International waters. So no one would have to ask them for permission, but that is the way it is and most do not risk it (insurance won't cover).
Nah, the narrowest points are below 24 nautical miles, so all ships need to pass through Iran and/or Oman's territorial waters (12 nmi each).
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> the strait is not Iranian property, but International waters
That seems to depend on who you ask. Iran has expressed a differing opinion on the matter and appears to be capable of striking the area in practice.