Prof. JRK mentioned that for BSDFs, it takes into consideration the entire 360 degrees. So I'm assuming that for BRDFs we don't need to take into account all directions, instead only directions that come out from the surface of interest.
Yes. In essence, BSDF takes into account transmission through surfaces where the BRDF does not consider them.
I found this interesting article that talks about how for a BRDF to be considered physically plausible, it should satisfy two conditions:
(1) Reciprocity: The incident light direction(l) and reflected light direction(r) for a BRDF(f) is the same after the incident and reflected direction is swapped. i.e. f(l, r)= f(r, l)
(2) Energy Conservation: Energy Conservation: The total energy of reflected light is less than or equal to the energy of the incident light. i.e.