Another shortcut for quadratic and cubic terms for continuous variables is to insert poly(var, 3) in your formula, which simplified how many interaction terms you have to specify! You are welcome, as so are upvotes ; )

No problem. It is actually straightforward and there are a few helper functions beyond specifying your own with n-1 vectors grouped with cbind. The "ordered" class has built in contrasts: var <- ordered(var). Get them with contrasts(var), which you can also use to update the contrasts. Default of ordered categorical is contr.poly, i.e. polynomial (quadratic, cubic and so on until n - 1) and there is some kind of weighting. You can specify helmert: constrasts(var) <- contr.helmert(n) or contr.SAS or contr.sum