Is testing easier/harder than learning?
If the learning algorithm is proper (i.e. it always produces a hypothesis from the class $F_n$), then it also gives a testing algorithm -- simply run the learning algorithm, and see whether the hypothesis it produced has error rate $&lt;\epsilon$, which can be done with only $\approx 1/\epsilon^2$ samples. If it does, since the hypothesis is in $F_n$, this is a constructive proof that the function you are testing has distance at most $\epsilon$ from $F_n$. If the algorithm was a PAC learning algorithm for $F_n$, then when $f \in F_n$, it must generate such a hypothesis. So any proper learning algorithm can be converted to a testing algorithm with only an additional $\approx 1/\epsilon^2$ samples at most. 

Moreover, if you are only worried about sample complexity and not computational efficiency, then without loss of generality you can always use a proper PAC learning algorithm. Since the sample complexity of learning is $\mathrm{VCDIM}(F_n)/\epsilon^2$, this means you can always test with at most this many samples. 

However, generally testing is easier than learning. For example, linear functions in $d$ dimensions require $d$ samples to learn, but only a constant number of samples to test.