You forgot Taiwan, who is faring much better than all three of the countries you mentioned.
What mostly helped was lack of mainland Chinese people entering the country. Also Taiwanese wear their face masks religiously and are used to obeying the rules set by the government.
Finally (AFAIK) they have a very good health care system which handled the cases quickly and efficiently.
If the whole world closed their borders to China back in early Jan (and followed up with tracing and quarantine), we would be seeing this right now. Unfortunately, China was lobbying heavily against it.
Now China, being a massive exporter, has a global demand problem in addition to the local supply problem of shutting down their country for 8 weeks.
N95 masks, fitted properly, do help prevent catching the virus. For a mask to be called N95 it has to be approved by the CDC. It’s specifically designed to block >95% of airborne particles. That’s why they’re recommended for caretakers at hospitals and frontline workers dealing with infected patients. Replaced every ~3 hours and worn in combination with goggles and ear protection, they minimize the risk of infection through mucosal membranes. They have also been in short supply.
Surgical masks do not prevent catching the virus, but they help sick people not to spread it due to the mask catching some of the spray droplets when they cough / sneeze
That's not true at all. There is a reason why surgical masks are used by surgeons, but for the protection level needed by medical professionals, it is used as a part of a wider system.
Used casually it prevents much of the droplets in the air from entering your respiratory system, as well as preventing a lot of touching of the face. There are studies that indicate wearing a mask decreases virus respiratory several-fold.
The reason the N95 filters work is because when the air is sucked in, it must pass through the filter before entering your respiratory system, and that filter is designed to filter >95% of airborne particles (and often times even higher). For the surgical masks, the air just gets sucked in from the side, the path of least resistance. So the airborne particles would also just get sucked in from the side. The masks may cause changes in behavior that lead to lower infection probability (such as reminding you not to touch your face), but dipping your hand in glitter would be just as effective.
Very early on they instituted a 14-day quarantine period for anyone arriving from mainland China (later expanding this to Hong Kong and Macau), Korea, Italy and Iran. As of today, this now applies to the entire Schengen area (i.e., most of the EU).
The government has also taken over mask production (increasing capacity) and distribution (with a rationing system and an online map of where they can be bought).
Their website is very informative, with very transparent information about how many have been tested, confirmed, recovered, etc.: https://www.cdc.gov.tw/En