proxima Campano ponti quae villula, tectum
praebuit et parochi, quae debent, ligna salemque.
Near to the Campanian bridge [ is ] an [official] hostelry, which
gave shelter; and purveyors [ afforded ] firewood and salt, which things [quae] they-are-responsible-for [debent].
I think I have this about right, but I had to work on the two relative pronouns.
Here are my constructions of the two relative pronouns.
quae … tectum praebuit: quae here is feminine singular nominative, agrees w. villula. It is the subject of praebuit.
quae debent: quae here is neuter accusative plural, antecedent is ligna salemque. It is the direct object of debent.
proxima Campano ponti quae villula, tectum
praebuit et parochi, quae debent, ligna salemque.
The main verb here is praebuit, and it serves as the verb of two main clauses, with villula and parochi as subjects – almost a zeugma. Actually, of course, the verb with parochi as subject would be praebuerunt, but this is wittily compressed so that a single word serves as the verb of both main clauses.
The first relative clause is proxima Campano ponti quae [est]. You’re correct that villula is the antecedent of quae, but your translation switches the (understood) verb of the relative clause with the main verb. Praebuit has to be the main verb, not the verb of the relative clause, because it also has to serve as the main verb of parochi . . . ligna salemque, so that the two main clauses are parallel.
Hylander’s right of course, but villula is actually drawn into the relative clause: quae villula (est) proxima Campano ponti. Now you know how to say The little house on the prairie: quae villula est in campo.
And an equally good way of construing parochi, quae debent, ligna salemque is to take quae debent as direct object and ligna salemque as being in apposition to that: “and the parochi (provided) what it’s their duty (to provide), (namely) fuel and salt.”