The Muzio is irrelevant. 4.Bc4 is a poor move (better are 4.h4 or 4.Nc3), and so is 4...g4 (better are 4...Bg7 or 4...Nc6).
Muzio Gambit

The Muzio is irrelevant. 4.Bc4 is a poor move (better are 4.h4 or 4.Nc3), and so is 4...g4 (better are 4...Bg7 or 4...Nc6).
There are many players who do not know the Bc4 line, so this could be used to confuse the opponent.
While for Bc4 and Nc6 , d4 is very strong, followed by c3 and Qb3.

The thing about the Muzio is that once you sac the Knight, you are committed, so you must keep the initiative at all costs. White does get compensation in the form of a strong attack against f7. If that style of play appeals to you, go for it! Whether you win or lose, it's a great way to practice tactics and attack.
There's also the Wild Muzio, which, if I remember right, is 1.e4 e5 2.f4 exf4 3.Nf3 g5 4.Bc4 g4 5.O-O gxf3 6.Bxf7+ Kxf7 7.Qxf3 saccing a second piece to pull the Black King out into the open. I think a young Kasparov analyzed it to a win for Black, but it's a dangerous line unless Black knows his stuff.
Qb3+ is bad there. 2... Qe6 and all you've done is help Black clear the royal pin on the f-file. To avoid a Queen trade White will have to move the Queen again.

Qb3+ is bad there. 2... Qe6 and all you've done is help Black clear the royal pin on the f-file. To avoid a Queen trade White will have to move the Queen again.
Then there is d5 followed by Rxf4+
I'm not following you. From your diagram if 2... Qe6 3. d5 Qb6+ 4. Be3 seems best, and then Black trades Queens with 4... Qb3 and do you mean 5. Rxf6+?. Black is winning there. I don't understand the notation Rxf4+ for either player there. Black has no rook attacking f4 and White can't capture his/her own Bishop.
Such a brilliant gambit for hyperaggressive players but not so popular. I wish it was more recognised.Ithink you would like exploding game between Karpov and Dimnov.
So please let me know if ther is there any mistake in this aggressive opening (hyper).Even Nakamura and Shirov use it occasionally to surprise their opponents.