Adverb word order
I'm aware that Esperanto is fairly relaxed when it comes to word order, but I was wondering if there are any hard and fast rules in regard to the placement of adverbs in a sentence?
Adverbs generally go before the word the modify. They can also go at the end of a sentence.
Neither of these rules are hard and fast.
I think it depends on the adverb in question. "Nur" for example MUST go immediately before the word it modifies to convey the proper meaning: Nur mia patro piediras al la oficejo. is quite different from "mia patro piediras nur al la oficejo, and both are diferent to "mia patro nur piediras al la oficejo"
Again, these rules are not hard and fast. I agree that "nur" is much less likely to be found at the end of a sentence than "rapide" is -- but you will find "nur" at the end of some sentences. For example, the title of Sten Johansson's book: Neĝo kaŝas nur.
None of this changes what I said originally, that that's that adjectives (like "nur") generally go before the words they modify, as your examples demonstrate.
A sentence like "mia patro iras piede al la oficejo nur" does indeed sound strange to me, and might not be 100 percent clear, but I would understand it based on semantic cues. "My father goes by foot only to the office."