I don't see any problem here, nor any problem with Stockfish's evaluations.
1: e4 e5 2: h3 (0.00)
This is a completely correct evaluation. White hasn't made any mistake at all, h3 is a perfectly unobjectionable move. However, he has given up his first-move advantage by not playing development. Of course, this move is completely objectionable in the sense that white could have played something much better (2: d4 2: Nf3 2: Nc3 2: f4 2: Bc4 etc.) but it doesn't give black a weakness to a attack or a positional help, which is why I said it's "unobjectionable". It just wastes a move that white could have used on something better and equalizes the position that was previously in white's favor.
This is true in all of the 2: h3 moves the computer gave as equal (or sometimes +0.1). The position is solid, so it doesn't do anything to help the opponent, but it wastes a move that could have been spent on something better and gives up first move advantage.
h3 is a BAD move (rather than just a waste of a move) in open or sharp positions where white's tempi need to be used constructively. For example, 1: e4 e5 2: f4 exf4 3: h3. This move is extremely bad because the position is sharp and demands immediate action from white. He can't afford to waste a move. I'm guessing 3: ...Qh4+ is a good way to continue.
However, in positions where tempi come at a pretty low cost, rook pawn moves aren't bad at all, they just waste tempi and give up advantages centered around tempi.
stoxfish found you are an awesome player so he had choosen defensive variation h3 and a3 sops night op to certain point and it is considered as per chess convention as a defensive move and weakening castled king or queenside etc. however if u have idea how to defend it where opponents want to exploit it . can you please share that ?
There's nothing for black to exploit after 1: e4 e5 2: h3. The position is equal, white has given up his first move advantage and obtained equality. Black should simply make logical developing moves and once the middlegame is entered he will find himself with more options than he normally does.
love your posts though 
Note that online Stockfish engines are usually set to look a small number of moves ahead - if you set Stockfish to look deeper, it doesn't recommend weird moves.
For example, using the great free Lucas Chess, I set Stockfish 8 to look 30 ply head and up to 15 variations after each move. In the Indian, after 1 d4 Nf6 it likes 2 Bf4 best followed by 3 e3 and 4 Nf6 - basically the London System! Lucas's Standard Deepfish 7 - a variation of Stockfish that supposedly is great when looking for short-term tactics - set to 10 ply prefers 2 Nf3 then 3 Bf4 and 4 e3 - the London System itself!
Here's the Lucas Chess Analysis window: