Get well soon!
Basicaly, you have to DOW those first, then DOW a daimyo.
Nope, you can buy them for as cheap as 1 Infamy. But you have to make sure the Emperor is war leader, otherwise they'll cost you 4. Which can be a nuisance since Japan is often allied or guaranteed by Korea, Ming or Manchu.(Also, due to the diplomacy, provinces will always be at full cost [can only interact with the emperor, but must take provinces from the allied daimyos]). Japan is a nuisance.
Basicaly, you have to DOW those first, then DOW a daimyo.