You will definitely need a new police certificate (for each country you have lived in over 6 months since the age of 18), because police certificates are only valid for 3 months anyway. Buffalo will need the police certificate(s) and they have to still be valid when Buffalo receives them.
Medicals are only valid for 1 year, so that does depend on how long ago you got it and whether it is even still valid when your file reaches Buffalo. You'd probably still need to send PROOF of some sort to Buffalo that you had it done, even if it's already on file for your study permit. Even if it is valid by the time Buffalo gets your file, if it expires before they make a decision on your file (and no one can say for sure how long that will take), you will likely be requested to get another medical anyway.
If it were me, I'd get both new police certificates and medical done anyway. Better to be safe than sorry.
EDIT: Just saw in your other thread that your police certificate was issued back in June. Edited my post above to reflect this.