Wrong. Yes you can. You just can't buy/sell it at favourable rates. I just tried buying Yuan with my bank in Canada couple months ago, the rates are horrible.
You reported that you tried to buy Yuan at your bank in Canada and the fees are horrible, it doesn't impress me. In the foreign exchange market, the Yuan represents 4.2% of the total used, this may seem significant, but the Chinese currency is in 5th place, behind the leading dollar, the euro, the pound, the Australian dollar and the Canadian dollar. The Chinese currency is not yet fully convertible and the Chinese need a long way to become the main currency used in the forex market.
Again, having a freely convertible currency is not a prerequisite for reserve currency status. The main determinant is wide acceptance and use.
China still needs to change a lot before having its currency as the world's main reserve currency. China has made significant strides over the last decade to make this a reality, the IMF's acceptance of, for example, the Chinese currency in the IMF's SDR basket of currencies. The Chinese currency represents something around 10% of the currency basket, with the euro ahead with 30% and the dollar in the lead with more than 40% of its share in the currency basket. This may mean something, but it does not represent the real world of international reserves of the world's main central banks, even if the Yuan will considerably increase its performance in the IMF's SDR currency basket, it does not mean that the Chinese currency is being used in the countries' international reserves. The world today has a value of US$12 trillion as reserves, the Yuan represents only US$230 billion, something a little above 2%, as you can see, a very different percentage of the SDR's basket of currencies as a whole, the dollar represents half of all reserves, for the Yuan to dethrone the dollar as the main reserve currency, it will take many decades to be used as the main currency of the world's monetary authorities.
The use of the Chinese currency in the international market is also a percentage similar to the reserve currency status, somewhere around 1.91% of the total, well behind the euro with more than 36% and the dollar with more than 38% of the total of the currencies used, the Yuan is in 5th place, also behind the pound sterling and the Japanese yen, the problem is that China is the largest exporting country in the world and about to become the largest importer in the world as well, but even under these commercial conditions , its currency still has a negligible participation in global trade, even considering its gigantic economy. The data that impressed me the most was that, despite being the largest exporting country in the world, the currency most used for financing exports, the dollar continues to lead with more than 56% of the total, well ahead of the euro with 6% and the Chinese currency in third place with 2.22%.
Wrong again. If Chinese people can't buy and sell Yuan then how do they study and live abroad? Only the amount exchanged is limited, and it might take a week or two cause it requires government oversight.
The Chinese manage to send large sums of money abroad through unofficial channels, in reality this situation has been present since the capital control exercised by the Chinese. Through parallel channels, the Chinese send more than US$50,000 abroad, if you take the volumes sent abroad, you will see that the movement of capital abroad has not changed at all, there has only been a decrease in the movement of official channels , increasing the participation of parallel channels of exchange movements.
If U.S government forcing the banks to "voluntarily follow U.S law" is not a form of capital control. Then, what do you mean by capital control then?
The main monetary standard is the unit of account, and the dollar is the unit of account on the planet, this is the highest level of a monetary standard, think of everything that is currently priced in the international market, both financial and commercial, everything is based in dollars from commodities, oil, wealth, GDP and everything else that can be priced. The euro is not a unit of account, the pound sterling is not a unit of account, the yen is not a unit of account either, and the Yuan is clearly not either, if it is ever going to make it.
China is far from making its currency its reserve currency, and even further as its main currency standard. China needs to open its capital account, allow the free conversion of its currency, that means the Chinese cannot control the foreign exchange market, that is, assure investors that they can sell a Chinese government bond or a stock in a company and withdraw the amount whenever you want and in the volume you want, today there is no such free movement of capital. In the US, you can do as you please without having to worry about volumes, as there is no exchange control as it is present in China, which is why the world still trusts the dollar and not the Yuan, the dollar still has a lot of confidence that Yuan doesn't have. If that doesn't change, it's very difficult for the Yuan to be a global competitor to the dollar as the world's main currency in every way.