Tristram: In lower left corner, after 1. e3 2. d2, 3.f4 is at least as good as 3. b5. After 3.b5, 4.f4 5.e4 6.e2, W has to decide whether the c4 stones are worth sente.
d4rkm4tter: There is a typo in your sequence, but your question is if e3-d2-f4 should be correct too. Continuation would be b5-e2. If we assume that both sides are equally good, I prefer the correct solution, because it ends in sente or black walls off both sides.
In lower left corner, after 1. e3 2. d2, 3.f4 is at least as good as 3. b5. After 3.b5, 4.f4 5.e4 6.e2, W has to decide whether the c4 stones are worth sente.