No, they are not silent. Well that is not a rule, because there are places like in Cuba or Puerto Rico where the phonetics are different from mexican, or spanish spanish. I think that in several caribean places, they don't pronounce the "r" and the "s" or they pronounce them but very weakly.
In places like Veracruz, Acapulco or other places near the coasts of Mexico (I should say that they are beautiful places) , people don't pronounce some letters when they are talking.
Example:
At the city:
- ¡Vamos a la costa, a ver el mar!
At the coast (just pronounciation):
- ¡Vamoj a la cojta, a ve el má!
Or:
- ¡Vamo a la cota, a velmá!
I think there are plenty of variations, but i think that in short words the answer of your question is (taking on account what i've just said):
" The letters r and s are never silent, even if they are at the end of a word"
I should add, that the "h" is the only letter that is not pronounced as Vicky said.
Regards