user16626: Here are the first few moves:
1.c4 e5 2.Nc3 Bb4 3.Nd5 Bc5 4.Nf3 e4 5.d4 Bf8  
After the fifth move, black has essentially only pushed one pawn, while while has developed two knights and his c-pawn and d-pawn. However, the current position does not seem bad for black at all. 365chess.com gives winnings percentage White / Draw / Black as 25% /50% /25%.
[fen ""]
1.c4 e5 2.Nc3 Bb4 3.Nd5 Bc5 4.Nf3 e4 5.d4 Bf8

My question is, in the first few moves, has black violated any opening principles? Why this position is not too bad for black while he has only pushed one pawn while white has developed two nights (and it is white's turn now)?

user14079: In their recent book The Modern English 1.c4 e5, GM Kiril Georgiev and Semko Semkov consider the line 1.c4 e5 2.Nc3 Bb4 3.Nd5 (considered better than 3.Qc2) Bc5 (the alternative is 3...a5) 4.Nf3 e4, although their main variation continues with 4...c6.
They now recommend 5.Ng5! because

5.d4 is also possible, but after 5...Be7 we cannot put the knight on g5.

In the game you consider, Black obviously anti-developed with 5...Bf8?! (which indeed goes against the main opening principle) because he was afraid of losing the bishop pair after 5...Be7 6.Ne7.
However, after a further 6...Qe7 7.Nd4 Nf6 (or even Qc5 8.e3 Nf6), Black's faster development and space advantage likely compensate for the bishops.
On the other hand, 5...Bf8 6.Bf4 d6 7.Ng5 or 7.Nd2 yields a nice initiative to White. 

user11629: Obviously black has violated principles such as:

don't move a piece twice
develop pieces

However opening principles are just general guidelines and in very concrete positions like the one at hand they are of little use. There are many established openings where opening principles are broken, so nothing wrong with that.
In the final position it is white's move, however the knight on f3 is attacked and has to move. After the knight has moved, black will most certainly kick away the other knight by playing c6 and then create a strong pawn center with d5 or f5. 
White has currently a lead in development but black has more space and will have an easier development for its minor pieces than white. If there is nothing immediately threatening from white, I don't see why black should have a bad position.
Note that my engine still prefers white's position by about +0.5.

16626: <p>Here are the first few moves:</p>

<p>1.c4 e5 2.Nc3 Bb4 3.Nd5 Bc5 4.Nf3 e4 5.d4 Bf8  </p>

<p>After the fifth move, black has essentially only pushed one pawn, while while has developed two knights and his c-pawn and d-pawn. However, the current position does not seem bad for black at all. 365chess.com gives winnings percentage White / Draw / Black as 25% /50% /25%.</p>

<pre><code>[fen ""]
1.c4 e5 2.Nc3 Bb4 3.Nd5 Bc5 4.Nf3 e4 5.d4 Bf8
</code></pre>

<p>My question is, in the first few moves, has black violated any opening principles? Why this position is not too bad for black while he has only pushed one pawn while white has developed two nights (and it is white's turn now)?</p>
 14079: <p>In their recent book <a href="https://www.newinchess.com/the-modern-english-1-c4-e5" rel="nofollow noreferrer">The Modern English 1.c4 e5</a>, GM Kiril Georgiev and Semko Semkov consider the line 1.c4 e5 2.Nc3 Bb4 3.Nd5 (considered better than 3.Qc2) Bc5 (the alternative is 3...a5) 4.Nf3 e4, although their main variation continues with 4...c6.</p>

<p>They now recommend 5.Ng5! because</p>

<blockquote>
  <p>5.d4 is also possible, but after 5...Be7 we cannot put the knight on g5.</p>
</blockquote>

<p>In the game you consider, Black obviously anti-developed with 5...Bf8?! (which indeed goes against the main opening principle) because he was afraid of losing the bishop pair after 5...Be7 6.Ne7.
However, after a further 6...Qe7 7.Nd4 Nf6 (or even Qc5 8.e3 Nf6), Black's faster development and space advantage likely compensate for the bishops.</p>

<p>On the other hand, 5...Bf8 6.Bf4 d6 7.Ng5 or 7.Nd2 yields a nice initiative to White. </p>
 11629: <p>Obviously black has violated principles such as:</p>

<ul>
<li>don't move a piece twice</li>
<li>develop pieces</li>
</ul>

<p>However opening principles are just general guidelines and in very concrete positions like the one at hand they are of little use. There are many established openings where opening principles are broken, so nothing wrong with that.</p>

<p>In the final position it is white's move, however the knight on f3 is attacked and has to move. After the knight has moved, black will most certainly kick away the other knight by playing c6 and then create a strong pawn center with d5 or f5. </p>

<p>White has currently a lead in development but black has more space and will have an easier development for its minor pieces than white. If there is nothing immediately threatening from white, I don't see why black should have a bad position.</p>

<p>Note that my engine still prefers white's position by about +0.5.</p>
