It does, but the primary concern is iran stopping oil transit by other countries in the strait of hormuz, not their own oil.

Which they did just start to do.

China buys Iranian oil, if they’ll start to but oil from non-sanctioned countries it will push prices up. But the biggest reason for prices to go up is the risk that Iran will attack tankers in the strait of Hormuz or oil infrastructure on Arabian peninsula.

Yes, because if it stops flowing, demand on the public market will increase, and prices will rise.