Does the Solderer and what-not use the JSON recipe system in the MC 1.12 version?
No, not yet
In version 1.5.10 they will use JSON recipes, as the above commit.
Is it possible for other mods to make usage of the json recipes loader? Like, just putting some files under assets/mymod/solderer_recipes?
Not yet, I still have to make that happen somehow.
Don't want to open up another issue for this simple question. Was there a reason why the removeRecipe method has been removed from the API?
Yes, because the getRecipes return value in ISoldererRegistry is modifiable, so removeRecipe is unneeded.
Most helpful comment
In version 1.5.10 they will use JSON recipes, as the above commit.