I want to predict teacher judgment accuracy from predictors at student (dummy coded) and at classroom level (continuous) and possible interactions. I am thus estimating an intercepts and slopes as outcome model.
Also, I have a variable indicating how well the teacher knows a child. As teachers differ in how well they know the kids of their class (for various reasons), my approach was to group-center it and to integrate it at the individual level: [...skip usevar ...] cluster = classno;
within = kennkind sex_kid lang_kid ses1 ses2 ses3;
but instead you have to define a random slope for each of those 6 predictors separately. You don't have to define random slopes for all of them - in fact, I would explore the need for it for each at a time.
As for your last question, you may have the wrong predictors.