Question: 1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 Bc5 5. Nxf7 Bxf2+ 6. Kf1 Qe7

1) Chess.com computer at Level 10 plays 5. Nxf7. Theory recommends 5. Bxf7. Which line to follow in my game in tournaments? Please advice as I am confused now.

2) After analyzing the game with computer of chess.com it suggests 4. ... Bc5 as Blunder. The best move suggested by it is 4. ... d5. Again confused as I know that this theory is Traxler Counter Attack and another is going for main line of Two Knights Defense. Kindly give your valuable suggestion. I played this game just now with play computer option of chess.com without login but as a guest. Waiting for your valuable answers. Thanks in advance

Answer: 
Bxf7+ is definitely the way to go in practice in my opinion. I have done quite a lot of analysis with stockfish on Nxf7 and am not at all sure it is better for white despite the computer evaluation early on.

Bxf7+ almost certainly is a lot better for white and is a lot simpler to learn which is important for a repertoire choice against an unusual line (most people won't have the guts to play Traxler!)
As previously suggested by Hamish, Bxf7 instead of Nxf7 is a safe way for white to gain an edge, though Nxf7 is unsound anyways.

In my opinion, if you want a swashbuckling defense against the fried liver,

e4 e5 Nf3 Nc6 Bc4 Nf6 Ng5 **Nxe4!?**

This move is much less known than traxler counter gambit and full of tricks. For example, if

Nxf7, black is equal, if not better(Nxf7 wins for white in the traxler (see Saglione vs Moreno carretero or any chess engine)).
Nxf7 Qh4 O-O(best move is Qe2, very difficult to find because it invites Nd4) Bc5 (black is already winning) Nxh8 Nxf2 .... and that's just one of the lines.

But both of these lines are UNSOUND to Bxf7, so really you should play d5.
e4 e5 Nf3 Nc6 Bc4 Nf6 Ng5 d5 exd5 Na5 Bb5+ c6 and I'll let you investigate yourself, but this line is the reason why strong players seldom play Ng5.