Which gambits are the most sound?

Feel free to show us the "winning line" after 5...d6.

And 5.d4 isn't such a bad move: 5...Qh4+ (else Black is somewhat worse) 6.Ke2 d6 7.Nf3 Bg4 8.Qe1! etc- typical King's gambit structure.

whats your opinion on ponziani gambit? is it solid enough?

After e5 and nf3 how is white winning?

There is no “line”, white is just better. There are variations you can go into. But you’re the IM, so can you explain why white is not winning?

And, maybe not a “bad” move, but you just explained almost all gambits. Not bad, but compared to what you could have (with sound openings), it’s simply better. I’d rather have a knight on f3 than a pawn on d4 and a king on e2. 

What is the Marshall Gambit in the Triangle system? I've never heard of it before.

Let's extend this list to include gambits where the side playing them is no worse, which ones do you know of that fits this category? You said that if you extend it to include those types of gambits the list becomes much larger.

Is white always able to regain the pawn if black accepts the Vienna Gambit?

Yes except for daminao

That’s because it isn’t sound. An early e5/c5 and white is worse. The system with Nf6 and Bf5 is also quite bad, as a bdg player 

it's Blackmar, not Blackmere. Blackburne also used the Blackmar Diemer Gambit, although Armand Blackmar was the the first to employ it, Diemer started using it after Blackburne did.

Does anyone mind commenting on the “sound-ness” of

1: d4 f5 e4

and 

2. e4 d5 exd5 nf6

not quite sure where to put these

About equal with best play. In other words entirely sound.

Actually, even 1.d4 f5 2.g4!? is sound 

Not a gambit yet, and I'm not sure about the Nxd5 lines, but I'll assume you're talking about the portugese 3.d4 Bg4!?

Borderline sound - Multiple ways for white to get a small edge, but no definitive refutation. I would put it in the same category as BDG, maybe slightly stronger.

Yeah, Portuguese and Icelandic (I kinda group em together)

Speaking of the Icelandic, reminds me of another gambit, this one is completely sound.

Scandinavian gambit: 1.e4 d5 2.exd5 Nf6 3.c4 c6 and white's best choice is to decline the gambit and enter a Panov. If he takes the gambit pawn he is immediately slightly worse I believe.

The Queens gambit is the most safe gambit..

For gambits where you are not completely guaranteed you will get your material back or else get a winning advantage 

The best gambit is The King's gambit 

There is another gambit dubbed the Dark Knight Gambit by Levy Rosman.. check his channel to find out what it is about if your interested

If you play the Scandinavian. Take back the pawn with the queen.. Nf6 is not good.. 

Just because you moved your king in the opening for example Ke2 doesn't mean your opponents position is preferable. 

Even GM @Smurfo who wrote a whole book on it says that the Portuguese is objectively unsound.

Yeah, I don't have the book on me at the moment, but I seem to remember the first 4 words of the book were "this opening is unsound"

This is more from a philosophical point of view though, if you read further you will see that Smerdon makes a similar conclusion to my post #33. i.e. that he couldn't find any way for white to get anything more than a slight, but manageable advantage or something like that.

Although, apparently since the release of the book white has found some new ideas in the Correspondence refutation, so this might not be the case any more. I expect Smerdon to address these when he converts the book into chessable format in the near future.