Other than going to the supermarket once a week, she never goes out = She never goes out except go to the supermarket = She never goes out except going to the supermarket?
Other than going to the supermarket once a week, she never goes out = She never goes out except to go to the supermarket = She never goes out except [when / for] going to the supermarket.
She had done little to personalize her room, except hang a few posters on the walls.is fine as it is, as well as she did everything except draw pictures and The government has a few options except keep interest rates high.
A. (Are you sure it said a few?) In my opinion, it would be preferable to say few options except to keep the interest rate high. I think the to was omitted because the author was thinking of keep as an imperative.
The government has few options except (this): Keep the interest rate high.