Yeah, Hyojong had the plan but, by his reign, the Qing were already ascendant and fighting them after two previous losses, both within the last 30 years, would be poorly advised at best. In conjunction with the Revolt of the Three Feudatories, perhaps Joseon Korea could've seen some success but, again, the issue of actually holding the territory for long enough becomes and issue. Plus, Hyojong was long dead by that point and keeping a nation like Korea militarised would be difficult to maintain economically and socially.
Again, not really ever in the Joseon court's scope. The north of the peninsula is sparsely settled, trade with China and Japan far outweighed any ventures to the south in returns on investments plus provided any resource needs for the kingdom, and prisoners could just be sent to one of Korea's myriad of islands.
Again, too far, too pricey, too low expectations for success by the court to push for it and not enough adventurous merchants willing to go for it rather than just trade with China and Japan. Ryukyu's a Ming/Qing tributary, which makes that a bit more difficult, and Formosa was under the rule of the Portuguese, Dutch, or Qing, none of which Joseon Korea could go against and win.
As for Japan, Japan's navy was only better than Korea's after the Meiji Restoration so not sure where the incentive you're referring to is.
And again, colonial empires are expensive and often didn't give returns to justify the costs. Joseon Korea didn't have the desire to before the Imjin War and didn't have the funds to after it. And even if they did, what would come of it? The European colonial nations moved towards the world's biggest markets, India and China, for resources. Joseon Korea already is next to China, so expansion of trade's not something on most peoples' minds before the modern era.