Can i play the KIA against the Sicilian ?



Wrong!
The KIA vs Sicilian and the Closed Sicilian are NOT the same thing.
The Closed Sicilian sees the Knight go to c3.
The KIA sees the Knight go to d2
For example: 1.e4 c5 2.Nf3 e6 3.d3 Nf6 4.g3 g6 5.Bg2 Bg7 6.O-O O-O 7.Nbd2 d5 etc.
As far as whether it is playable against the Sicilian - ONLY the e6-Sicilians. Not the others as the Bishop can come out. The success of the KIA, similar to the Colle System, is reliant on the Black Light-Squared Bishop being trapped behind the pawn structure.

Wrong!
The KIA vs Sicilian and the Closed Sicilian are NOT the same thing.
The Closed Sicilian sees the Knight go to c3.
The KIA sees the Knight go to d2
For example: 1.e4 c5 2.Nf3 e6 3.d3 Nf6 4.g3 g6 5.Bg2 Bg7 6.O-O O-O 7.Nbd2 d5 etc.
As far as whether it is playable against the Sicilian - ONLY the e6-Sicilians. Not the others as the Bishop can come out. The success of the KIA, similar to the Colle System, is reliant on the Black Light-Squared Bishop being trapped behind the pawn structure.
What are your thoughts on the Delayed Alapin KIA-style structure? A line like 1. e4 c5 2. Nf3 d6 3. c3 Nf6 4. d3 g6 5. g3 Bg7 6. Bg2 0-0 7. 0-0 seems a reasonable try to play an opening similar to a KIA against a Sicilian without e6, as I don’t really think the addition of Bg4 at any point would be altogether too advantageous for Black.

Now I decided to go for the Moscow Variation against the 2. ... d6 Sicilian, and for 3. d3 against the 2. ... e6 Sicilian. That seems reasonable to me, but I don't know what to do against the 2. ... Nc6 Sicilian as the Rossolimo against 3. ... e6, 3. ... g6 seems too much theory heavy for me. Any suggestions on what to do against 2. .... Nc6 that is not a "meta"-opening but is playable ?

In the end, I think I will use the Delayed Alapin against 1. e4 c5 2. Nf3 Nc6 3. c3!?. Thanks all for the help.

Wrong!
The KIA vs Sicilian and the Closed Sicilian are NOT the same thing.
The Closed Sicilian sees the Knight go to c3.
The KIA sees the Knight go to d2
For example: 1.e4 c5 2.Nf3 e6 3.d3 Nf6 4.g3 g6 5.Bg2 Bg7 6.O-O O-O 7.Nbd2 d5 etc.
As far as whether it is playable against the Sicilian - ONLY the e6-Sicilians. Not the others as the Bishop can come out. The success of the KIA, similar to the Colle System, is reliant on the Black Light-Squared Bishop being trapped behind the pawn structure.
What are your thoughts on the Delayed Alapin KIA-style structure? A line like 1. e4 c5 2. Nf3 d6 3. c3 Nf6 4. d3 g6 5. g3 Bg7 6. Bg2 0-0 7. 0-0 seems a reasonable try to play an opening similar to a KIA against a Sicilian without e6, as I don’t really think the addition of Bg4 at any point would be altogether too advantageous for Black.
All you've done is throw in c3 with the Fianchetto of the kingside. The Bishop still comes out, and all you've done is mix ideas. The purpose of c3 is to play d4.
That is part of the flexibility of the KIA is you have the idea of blocking the center with e5 and a kingside attack, or playing c3 and going for the d4-break. Both really do require e6 by Black to be efficient.
Bg4 isn't the only problem. So is something like Bd7-Qc8-Bh3. Anything to trade that Bishop off to alleviate the space disadvantage.
Part of what makes the KIA work is the cramping of Black's position with all the material on the board. Think about the KIA vs French. It is very hard for Black to get his pieces to the rescue of his king. He can get a Bishop to f8, but then h7 is a problem. He can get a knight to f8, but then g7 is a problem. Also possibly f7 in both cases.
You want to keep pieces on, not trade off. It isn't about whether Bg4 or Bh3 looks dangerous. It is about the positional factors and Black's alleviation of the cramping and removing pieces from White's attack.
Think about other openings where White gets a space advantage. Advance French. Caro-Kann. KID 4 pawns attack. Exchange Grundeld. Who's usually looking to trade pieces and trying to achieve a favorable endgame? Black! Think about the exchange Grunfeld with White's big center and Black's Queenside 2-on-1. That 2-on-1 is most favorable in an endgame. Black's lack of space is a non-issue is he only has to maneuver 2 pieces instead of 7.
Now think about defenses where Black does not have a space disadvantage, but rather a weak square, like the Stonewall Dutch. Black wants to keep pieces on except maybe the light-squared Bishop.
So the KIA has 2 ideas - Kingside Suffocation and the central break, in both cases, White being the one looking to keep pieces on, and so again, you really need ...e6 from Black for it to work.
Think about 1.e4 e5. You ever see the KIA at the gm-level against 1...e5? No because the IDEAS behind the KIA rely on Black's lack of space and inability to trade pieces off. Black does not lack space after 1.e4 e5, and White's formation has no purpose. What are you doing with that Bishop on g2, pawn on d3, Knights on d2 and f3, if Black has an open game with his pieces easily able to find good squares after 1...e5? You have to change your tune and play the position and not think systematically like a robot.
The KIA has a specific purpose in mind and works in specific situations. It is not a "let's close our eyes and play e4/d3/Nd2/Ngf3/g3/Bg2/O-O against whatever Black plays, open our eyes, and play chess" type of opening. No opening is that way.
The London fails to the Modern Defense.
The old idea of Kosten's of play 1.c4/2.g3/3.Bg2/4.Nc3 against anything also fails as White has nothing against 1...e5/2...Nc6/3...f5/4...Nf6. As Marin points out, in the English, ...Nc6 in any 1...e5 defense should always be answered by Nc3. 1.c4 e5 2.g3 Nc6, the move 3.Bg2 is a mistake. 3.Nc3! Now if 3...Nf6, then 4.Bg2. But if 3...f5, then 4.Nf3! Nf6 5.d4! e4 6.Nh4 and if ever ...g5, then Ng2 and h4! Not possible with a Bishop on g2. Bishop will develop on e2 or d3.
You have to ask yourself what you are doing, not just try to find move order alternatives to try to force your cookie-cutter approach to work because more often than not, it doesn't work.
For the Colle, Catalan, and KIA, the crucial thing is that Black's LSB is blocked behind his own pawns.

Wrong!
The KIA vs Sicilian and the Closed Sicilian are NOT the same thing.
The Closed Sicilian sees the Knight go to c3.
The KIA sees the Knight go to d2
For example: 1.e4 c5 2.Nf3 e6 3.d3 Nf6 4.g3 g6 5.Bg2 Bg7 6.O-O O-O 7.Nbd2 d5 etc.
As far as whether it is playable against the Sicilian - ONLY the e6-Sicilians. Not the others as the Bishop can come out. The success of the KIA, similar to the Colle System, is reliant on the Black Light-Squared Bishop being trapped behind the pawn structure.
What are your thoughts on the Delayed Alapin KIA-style structure? A line like 1. e4 c5 2. Nf3 d6 3. c3 Nf6 4. d3 g6 5. g3 Bg7 6. Bg2 0-0 7. 0-0 seems a reasonable try to play an opening similar to a KIA against a Sicilian without e6, as I don’t really think the addition of Bg4 at any point would be altogether too advantageous for Black.
All you've done is throw in c3 with the Fianchetto of the kingside. The Bishop still comes out, and all you've done is mix ideas. The purpose of c3 is to play d4.
That is part of the flexibility of the KIA is you have the idea of blocking the center with e5 and a kingside attack, or playing c3 and going for the d4-break. Both really do require e6 by Black to be efficient.
Bg4 isn't the only problem. So is something like Bd7-Qc8-Bh3. Anything to trade that Bishop off to alleviate the space disadvantage.
Part of what makes the KIA work is the cramping of Black's position with all the material on the board. Think about the KIA vs French. It is very hard for Black to get his pieces to the rescue of his king. He can get a Bishop to f8, but then h7 is a problem. He can get a knight to f8, but then g7 is a problem. Also possibly f7 in both cases.
You want to keep pieces on, not trade off. It isn't about whether Bg4 or Bh3 looks dangerous. It is about the positional factors and Black's alleviation of the cramping and removing pieces from White's attack.
Think about other openings where White gets a space advantage. Advance French. Caro-Kann. KID 4 pawns attack. Exchange Grundeld. Who's usually looking to trade pieces and trying to achieve a favorable endgame? Black! Think about the exchange Grunfeld with White's big center and Black's Queenside 2-on-1. That 2-on-1 is most favorable in an endgame. Black's lack of space is a non-issue is he only has to maneuver 2 pieces instead of 7.
Now think about defenses where Black does not have a space disadvantage, but rather a weak square, like the Stonewall Dutch. Black wants to keep pieces on except maybe the light-squared Bishop.
So the KIA has 2 ideas - Kingside Suffocation and the central break, in both cases, White being the one looking to keep pieces on, and so again, you really need ...e6 from Black for it to work.
Think about 1.e4 e5. You ever see the KIA at the gm-level against 1...e5? No because the IDEAS behind the KIA rely on Black's lack of space and inability to trade pieces off. Black does not lack space after 1.e4 e5, and White's formation has no purpose. What are you doing with that Bishop on g2, pawn on d3, Knights on d2 and f3, if Black has an open game with his pieces easily able to find good squares after 1...e5? You have to change your tune and play the position and not think systematically like a robot.
The KIA has a specific purpose in mind and works in specific situations. It is not a "let's close our eyes and play e4/d3/Nd2/Ngf3/g3/Bg2/O-O against whatever Black plays, open our eyes, and play chess" type of opening. No opening is that way.
The London fails to the Modern Defense.
The old idea of Kosten's of play 1.c4/2.g3/3.Bg2/4.Nc3 against anything also fails as White has nothing against 1...e5/2...Nc6/3...f5/4...Nf6. As Marin points out, in the English, ...Nc6 in any 1...e5 defense should always be answered by Nc3. 1.c4 e5 2.g3 Nc6, the move 3.Bg2 is a mistake. 3.Nc3! Now if 3...Nf6, then 4.Bg2. But if 3...f5, then 4.Nf3! Nf6 5.d4! e4 6.Nh4 and if ever ...g5, then Ng2 and h4! Not possible with a Bishop on g2. Bishop will develop on e2 or d3.
You have to ask yourself what you are doing, not just try to find move order alternatives to try to force your cookie-cutter approach to work because more often than not, it doesn't work.
For the Colle, Catalan, and KIA, the crucial thing is that Black's LSB is blocked behind his own pawns.
Oh interesting. I see that I’ve been going about the KIA all wrong. I was under the assumption that White was trying to play some sort of Reversed Positional KID, not a Catalan-esque structure. Thanks for the help!
I'm trying to create an opening repertoire with 1.e4; I'm having problems with the Sicilian. I don't care if after ... d6 or ... Nc6 the KIA is less effective than against ... e6 because I don't even understand why. What move order should I use ? I even thought of using 1. e4 c5 2. d3 as a move order. Furthermore, to study ideas and plans what should I use ? Thanks in advance.