Hi Arstan,
I'm no expert on the Bird, but here are some of my thoughts on your game.
5. g3 loses a tempo. This is because if black does choose to play Qh4, you could always then play g3, forcing him to move back. There is no reason you need to play it now. He can now perhaps put his queen elsewhere, in a more effective location.
Correct me if I'm wrong, but one of the themes of the Bird is to develop the light square bishop to d3. That way, you will have to bishops raking black's kingside, preparing for an attack.
9. a4 again loses a tempo, because Ba3 can easily be dealt with. If you are not being attacked, it is better to start an attack of your own. Perhaps 9. Bh3 and then 0-0-0 is better.
Hope this helps
A little bit about myself - I love gambits, but the idea that I'm playing something theoretically unsound bugs me sometimes. Not a lot, but a little bit.
So, I'm trying to expand my openings.
I'm very interested in the Bird opening and I'm enjoying playing it although sometimes I feel a bit confused after the first 10 moves or so. Oftentimes nothing has been taken at that point and all the pieces, except perhaps the queen's knight have been developed.
I think I'll start posting some of my games to see if you can help me learn how to play this opening better.
Anyhow, I just had a rather exciting game with the Bird opening that unlike most of my Bird's opening games had early fireworks and still resulted in a win for me.
I'm sure I didn't play perfectly, but I'm happy with the result here. Any feedback is appreciated.