I wonder how can black play tango if white plays catalan and plays c4 after castling?? Is tango possible??

I think the reply I had looked at was 5...Na5 6.e3 [not sure there isn't better perhaps] Bd6!? [more active and allows ...Qe7 to pressurise b4] 7.b4 Nb7 8.Nc3 a5, when black seems to have reasonable play, e.g. 9.Rb1 [probably the wrong move positionally] Qe7! 10.Qb3 ed 11.cd ab 12.ab O-O with control of the open a-file and a quick ...c5 coming to break open the position.

I have a feeling that 6.Nc3 is more critical, intending 7.e4 and trying to cast doubt on the validity of ...Bd6, eg 6.Nc3 Bd6 7.e4 when black can try the dangerous 7...exd5 8.e5 [8.cxd5 O-O looks fine to me] Bxe5!? 9.Nxe5 Qe7 10.Qe2 d6 11.Nd3 dxc4 12.Qxe7+ Kxe7 13.Nb4 Nb3 14.Rb1 Bf5 with unbalanced play, or the more solid 7...Ng4 which certainly does give white his edge.

I've even toyed with 7...O-O 8.e5 Bxe5 9.Nxe5 exd5 10.Nf3 dxc4 giving black three pawns for the piece and some imteresting chances, though I doubt it is fully sound.

However, I'm not sure the line can be dismissed so quickly just on the strength of 5.d5 - black does have his resources!

Regarding the 4.a3 variation, when I came out of retirement last weekend at the 4NCL I faced this on the sunday against a 2200 player. I replied with the (apparent novelty, according to my databases) 4...b6, and obtained an interesting position:

1.d4 Nf6 2.c4 Nc6 3.Nf3 e6 4.a3 b6!? 5.Nc3 Bb7 6.Bg5!? Ne7!? 7.Qc2 [logical, covering the e4 square] h6 8.Bh4 g5!? with sharp and combative play.

I in the end comfortably drew this and really should have played for the win. However, my opponent refrained from an early e4 which seems critical. 

Has anyone seen this line before? How would people improve white's play to secure an edge? We felt that white's position is aesthetically better here but it doesn't really offer a great amount, and black always seems to have resources if the game becomes prematurely open...

Yes, the prodigality with tempi is rather amazing (even if one can obviously rationalise it in various ways)! This might seem to suggest that White should try looking for an advantage in the 8 Bg2 variation, but it seems that here 8 ...0-0 9 0-0 (9 Nd2 Nd7!?) h6 has held up pretty well, and Black also has a decent score after 9 ...c6!? though the sample isn't large.

I guess 1 d4 Nf6 2 c4 Nc6 3 Nf3 d6 4 Nc3 e5 5 g3!?, as recommended by Richard Palliser, is also critical (and complicated!). Here the last time I looked I thought 5 ...Bg4 and 5 ...ed merited attention as well as 5 ...Bf5. Of course, in the Old Indian move order Black has to contend with 4 d5!? as well, but even if that's dangerous, we 1 ...Nc6!! players might just bypass it completely ...

No I hadn't looked at either of these. Both your suggestions look v. interesting to me! (I suppose 10 Be3 Ng4 11 Bd2 a5!? 12 h5 Nc5 13 Nh4 Nf6 [u]14 Qc2[/u] is possible but Black castles and strongpoints the dark squares?) Meanwhile I remember that last night I'd thought 10 Be3 Ng4 11 Bd2 [u]c6[/u] looked OK after 12 h5 Qb6 or 12 0-0 Ngf6.

The invention (8 ...Nf8) of the young Norwegian computer programmer looks more and more interesting! I wonder what he thinks about it ...

Did anyone of you look at 9.Be2 Nfd7 10.Be3 a5 11.Nd2 Nc5?

I think this looks quite promising. If White plays 12.g4 then 12...h6! seems quite strong.

I am sightly more concerned about 12.Bxc5!? but White really needs to know what he's doing to play a move like this, otherwise he could simply end up worse.

(1.d4 Nf6 2.Nf3 d6 3.c4 Nc6 4.Nc3 e5 5.d5 Ne7 6.e4 Ng6 7.g3 Be7 8.h4 Nf8 9.Be2 Nfd7 10.Be3)
Regarding 10...Ng4 11 Bd2, I was reasoning that after something like 11...0-0 12.h5 a5 13.Nh4 Ngf6 14.Be3 White achieves a nice setup anyway, but that rather begs the question if that is a problem for Black with light-squared bishops still on as you say. Perhaps Black is just fine here! I'm also just exploring!   
10...c6 11.g4 Ne8 12.g5, I was thinking Black could play on the queenside with eg a5/Nc7/Na6/Ndc5/Bd7 and if White plays f4 at some point, then exf4 and f6.

I had looked at 12.g4, but concluded that after 12...Ne8 White doesn't have the promising f4 plan as in Rohde-Hagesaether. I also looked at 11...Ng4, but what is the knight doing there after 12.Bd2? It will have to retreat at some point.
But perhaps you're right that Black can allow h5/Nh4/Nf5. I didn't like it, but I'll have another look.