Can´t say I´ve ever seen it, and looks horrible (from both of you, pardon me ... ) ... if he wants to give you the centre from the word go, why don´t you accept it joyfully with 1 ...e5 or ...d5? No hard feelings ...
What is this opening called?

It's called Van der Grujt or something on the chess.com explorer, a mouseslip opening basically.
Why would you play d5 in 2 moves?
I don't think it has a name. e3 and g3 don't really mix well. White is weak on f3 and h3, the light squares arond the King. If White can play f4 he'll maybe be ok. As Black you can take advantage of this if you can trade out the Fianchetto Bishop which is the main defender of those squares. A plan for that would go something like e5, Be6, Qd7, Bh3, h5-h4-etc... obviously White has moves in between but I don't think it's sharp or that it makes any sense to look at something like this move by move; just the general plan might help you, though. The way the game turned out I think taking your time in the center, d6-d5, and letting your opponent get e4 in added up to White being a bit better out of the opening... Black has problems with the light squared Bishop hemmed in by c6 and e6 until White was kind and played 25. d5... though I don't think Black's play in the opening was particulalry bad considering White's play and obviously the game was not decided in the opening at all.
Your dubious position out of the opening wasn't really anything to do with him. You just played weird moves, and although you won the game you were at best in a drawn endgame until he basically mated himself.
1. e3 is Van 't Kriujs' Opening, which I think is what Scottrf is referring to. http://en.wikipedia.org/wiki/Van_'t_Kruijs_Opening It's a transpositional tool, meaning players use it to get into other openings when they want to avoid certain variations or for other reasons... even Kasparov has played it. That's not what's going on here, though as g3 changes the game substantially, and does, as some have said "look like your opponent has made it up on the spot." I'd be surprised if it had a name.

1. e3 followed by 2. c3 is just a bad choice of the way to play the first two moves in chess and thus very probably does not have a name.
This has no name because no good player would play it.
You need to study basic opening principles, because you don't follow them here. At least three of your first five moves are dubious if not downright bad - and not bad for any deep hidden reasons, bad because they violate the basic fundamental opening principles of chess. This is the kind of chess 101 stuff that you should have learned as soon as you knew how the pieces moved.
Despite all that, you could have seized an advantage with 10. ... e5! instead of wasting even more time with ...a6.
Go read Chernev's "Logical Chess, Move by Move."
I agree

Not considering the very first moves, which have no independent value, white is either playing a home cooked Colle with fianchetto or a Catalan with c3 instead of c4. Black responded very poorly. e6 was OK, but after that you could have done d5 and possibly even c5. Then in a few moves you can also throw in e5 if applicable. That's the standard way to dismantle the Colle and I think it will certainly work if white used another tempo on g3.

This guy has an opening at least I haven't seen before. Any of the higher ranked players care to help? I played this as black. He beat me with this opening rather easily before I wisened up and pulled a game back.
And how about it ? What is this opening called?
http://www.chess.com/livechess/game?id=648028475
http://www.chess.com/livechess/game?id=647142848

This guy has an opening at least I haven't seen before. Any of the higher ranked players care to help? I played this as black. He beat me with this opening rather easily before I wisened up and pulled a game back.
Based on your game editor at #1. I wanna know how about the alternate moves like it ?
All openings result in 1 out of 6 characteristic pawn structures. The pawn structure after 13.Bxe3 is called a Jump Formation. The reason for the name derives from the fact that White's head pawn at d4 is a N's jump away from Black's head pawn at e6. Another characteristic of this pawn formation is that there are no pawns on the 5th rank. This a pawn structure that could result from a poorly played Semi-Slav or a botched French exchange variation.
The key to any pawn structure are the indicated pawn breaks. For Black there is an indicated pawn break with ...c5 and one contr-indicated pawn break with ...e5. For White There is one indicated pawn break at f5, and 2 contra-indicated pawn breaks (b5 and d5). Black has the half open d-file, White has the half open e-file. Black would like to post a N on d5 and White would like to post a N on e5. The strategic technique in both cases. If Black can post a N on d5, White can play c4 in order to kick the Black N from that post which would result in a pawn at d4 that cannot be defended by another pawn on a half open file that Black can attack. The better method for White would be to exchange the Black N at d5 so that the resulting exchange (...cxd5 or ...exd5) would leave a Black pawn occupying d5. Black' s strategy regarding White's N posting on e5 would be the same as detailed above.
If you would like to know more please let me know.

Some good books to solve AxKs problems have been suggested here.In addition, I would suggest a chess playing program,such as CM 10k or the like,the idea is to review any opening move that you played poorly against and find the proper way of handling such moves in the future.Reviewing entire games on a chess engine is also an excellant way to spot tactical blind spots.If you are an experienced player and are facing an opening that you have never seen before,it is probably utter junk.These openings typically involve unsound play,if you can spot it you will have the advantage.If you review these games with a chess engine your first loss to them will also be your last.

All openings result in 1 out of 6 characteristic pawn structures. The pawn structure after 13.Bxe3 is called a Jump Formation. The reason for the name derives from the fact that White's head pawn at d4 is a N's jump away from Black's head pawn at e6. Another characteristic of this pawn formation is that there are no pawns on the 5th rank. This a pawn structure that could result from a poorly played Semi-Slav or a botched French exchange variation.
The key to any pawn structure are the indicated pawn breaks. For Black there is an indicated pawn break with ...c5 and one contr-indicated pawn break with ...e5. For White There is one indicated pawn break at f5, and 2 contra-indicated pawn breaks (b5 and d5). Black has the half open d-file, White has the half open e-file. Black would like to post a N on d5 and White would like to post a N on e5. The strategic technique in both cases. If Black can post a N on d5, White can play c4 in order to kick the Black N from that post which would result in a pawn at d4 that cannot be defended by another pawn on a half open file that Black can attack. The better method for White would be to exchange the Black N at d5 so that the resulting exchange (...cxd5 or ...exd5) would leave a Black pawn occupying d5. Black' s strategy regarding White's N posting on e5 would be the same as detailed above.
If you would like to know more please let me know.
where does a person learn this stuff from? 'Jump structure' and 'pawn breaks'. Is there a single book that teaches this to a beginner like me (playing chess badly for a year.already have bad habits from playing too much too fast, without learning anything. Now slowing down and studying tactics puzzles...)
ah, I see the gentleman and scholar tmkroll has posted a strategy video. just beginning to watch it now...thanks Ty.
This guy has an opening at least I haven't seen before. Any of the higher ranked players care to help? I played this as black. He beat me with this opening rather easily before I wisened up and pulled a game back.