Exactly because of the English etc. I never bothered about move order issues and just played the standard IZ setup. It has served me quite well for more than 10 years.
1.c4 f5 2.Nc3 Nf6 3.Nf3 d6 4.d4 (indeed, or Black might play ...e5) e6 5.e3 Be7 6.a3 can be reached by 1.d4 e6 2.c4 f5 3.Nc3 Nf6 4.a3 (prevents the recommended ...Bb4) Be7 5.Nf3 0-0 6.e3 d6
a)7.b4 and Ne4 has been played; its strength depends on 8.Nxe4 fxe4 9.Nd2. If White can finish development and play f2-f3 he might be a little better. In this type of position Black has some problems finding good squares for the queenside pieces. So I would prefer 7.b4 Qe8 8.Bd3 Be8 and 9...e5.
b)7.Bd3 Qe8 8.0-0 Nc6 9.e4 fxe4 10.Nxe4 e5.

Black has more problems if White concentrates on quick development:
1.d4 e6 2.Nf3 f5 3.e3 Nf6 4.Bd3 Be7 5.0-0 0-0 6.c4 d6 7.Nc3 Qe8 8.e4 Van den Berg-Burstein, Tel Aviv 1958.
Perhaps Black might try 6...Qe8 7.Nc3 Nc6 8.e4 (8.d5!?) fxe4 9.Nxe4 Nb4 10.Bb1 Nxe4 11.Bxe4 d5 12.Bb1 dxc4 13.Qe2 Nd3.

One thing to remember is that all white setups have to be taken seriously. Black never can afford to play sluggishly. The first 6 moves are easy, but then you will have to answer two questions:
1) how to develop the queen's wing?
2) how to get ...e5 in?
Find the answers and you are usually OK.

It´s a long time ago I played this line with Black. If White didn´t play an early g3 I usually avoided e6. In the position after 4.d4 Black has an interesting alternative in 4... Nc6!?, the so called Krause-System, aiming for an immediate e5.

Regarding your question about the position after 6.a3 I don´t understand the intention behind this move. If b4 is the idea this can be played immediately without further preparation. Following 6... 0-0 7.Bd3 Black may try to prepare e5 with 7... Nc6. After 8.e4 fxe4 9.Nxe4 Nxe4 10.Bxe4 Bf6 looks okay for Black who can also try d5 on his next move.

Perhaps you can show some more moves of your games?