Still in house, ex left, she is advertising for a room to pay her part of mortgage. Do I have to allow?

This requires that an attorney examine your property division portion of your divorce. Common sense says she can't do that but the law is not always the best example of common sense. In most cases the house would be awarded to one spouse who would have to buy the other out. If you were both ordered to pay 1/2 the mortgage there must be an agreement about who has the right to occupy the house. If it's you you can refuse her attempts to rent out part of it. If this is not covered by the divorce agreement you should seek to have it modified.