Your understanding for 式 and 風 is correct. What I mostly hear about Japanese-style toilette in Japan is 和式トイレ (和=日本) (日本風トイレ is also fine though). 日本風/和風トイレ could refer to anything; the wall and/or toilette bowl itself and/or something else. Other examples are; 和食=日本食; this exactly refers to Japanese-type/style meal/food. 和風/日本風料理 could refer to that the taste of the food or atmosphere of the restaurant is arranged for the country. I often hear スペイン風/イタリア風居酒屋 in Japan (風 refers to food? atmosphere? maybe both). Anyway, hope this helps.