How to counter black’s early e5 on the Stonewall?


Why not play f4 instead of e3? then play e3 later?
In order to free the white bishop, as to place him on d3 and not allow black's white bishop to control the diagonal
No reason to play f4 to prevent e5; e5 simply loses a pawn and you should be happy to be up material 3 moves into the game. Just keep developing pieces normally afterwards

You could ignore the pawn with 3. Nf3 and turn it into a reversed French Defence, up one tempo which seems interesting (and kind of confusing). Capturing the pawn is best as mentioned by @blank0923.

imo if your opponent hangs a pawn for no reason in the opening you should take it
but if i am wrong, @exceptionalfork can correct me

What if 1.d4 d5 2.e3 Nc6 3. Bd3 e5, in other words, Black played Nc6 followed by e5. If white takes dxe5, back takes with Nxe5, threatening to take the Bishop on d3, which I believe is important in controlling the diagonal. What can white do to prevent black's e5 as the Stonewall structure is now gone, and what should white do from here?

What if 1.d4 d5 2.e3 Nc6 3. Bd3 e5, in other words, Black played Nc6 followed by e5. If white takes dxe5, back takes with Nxe5, threatening to take the Bishop on d3, which I believe is important in controlling the diagonal. What can white do to prevent black's e5 as the Stonewall structure is now gone, and what should white do from here?
3.Bd3 isn't something that White could consider, unless he is happy with 3.Bd3 e5 4.Bb5!? which is a reversed French Winawer (no tempo gained for White, as the bishop went at b5 in two moves).
But anyway, 3.c4, 3.Nf3 and 3.Bb5 make more sense- the first two will transpose to a not-so-critical line of the Chigorin Defense of the QGD.