I can help with the King's Gambit. Castling is not your priority. You want to launch a kingside attack, but first you need to strengthen your kingside and challenge white's center. If you want to see a good game for playing black, you can check out my current correspondence game. I play against it a lot so I've learned all the theory up to move 15 or so.
Crushing The Gambits. How?
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Link to your games, Charetter?
I've come across the Danish gambit, on the odd occasion; often the only real problems (I've seen at least) arise from White via Qe4 mating tactics (and pushing the central pawn with tempo). I'd probably respond with a quick Qb4, Ne2 and simply make use of the queenside majority.
Also, in the King's gambit, the following seems to often be overlooked by my opponents (at least in blitz games).
I have a third game that's still in progress. I'll post it after it's done. You can look at it by going to my profile, clicking games, and looking at my current games.
Here we go...
1. Danish Gambit :
The main line for black is this one
But nowadays, almost everyone go for this :
2. King's gambit :
The line u propose for white is bad, h3 being a useless move, never lose a tempo when u play a gambit! White just have to develop, Bc4, d4, Nc3, and even h4 are all playable.
In this gambit, if black can finish development, he will be extra pawn for nothing. So here, u played g5, continue to develop with Bg7 to secure your short castle, then u will prepare this castle, with moves like h6 (u have to protect g5 before moving Ng8), then maybe d6 and Nf6 (d6 to prevent e5, but not sure it is so good for white anyway...
We could have a long look and long variations on all this but u need simple things i think.
3. Halloween gambit : The best way in my opinion is to return your piece back to achieve development.
There are several lines, u can tranpose into 4 knights variation with 1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 4.Nxe5 Nxe5 5.d4 Nc6 6.d5 0-0 and after 7.d5xc6 b7xb6 u tranposed into scotch 4 knights...
But u can play more ambitously, several ways, but in your final position, u can give your knight, with Bc5 or Bb4 followed by castle. For example :
If u dont like this, u can chose 8...Bb4 9.exf6 Qxf6 with easy play too, more secure.
4. Latvian Gambit :
More simple is taking e5, because 1.e4 e5 2.Nf3 f5 3.e4xf5 e4 leads to wild play (and it sets problem, for example, where do u move your f3 knight now?) and its what really want die hard latvian gambiters.
So 3.Nxe5, u threat Qh5, best for black is Qf6, then d4 is playable but anyway u will have to replay your knight e5 (d6 will atack him), i prefer directly 3.Nxe5 Qf6 4.Nc4 f5xe4 and here lets continue to develop gaining tempo, 5.Nc3 attacks e4, Qf7 (5...Qg6 6.d3! e4xd3 7.Bxd3 Qxg2 8.Qh5 g6 9.Qe5 followed by Be4 and Qxh8 wins on the spot) and now we have to take care of a fork if black plays d5 Ne3 d4, so lets anticipate this : 6.Ne3! black cannot play d5 and we will play d3 or even Be2, 0-0, f3 opening f file in front of black queen. White can be satisfied...
That will cost you 30€ for the lesson, thanks lol 
As promised, my third game against the King's Gambit.
Is it possible for black to keep the -2 advantage in the Danish and administer a strong defense?
I dislike gambits especially against stronger players. Pawns are important. Gambits can be fun though. Remember to have fun when playing chess. www.JoyofSatan.org
"In the laboratory the gambits all test unfavorably, but the old rule wears well, that all gambits are sound over the board." - William Ewart Napier
A lot of times here on chess.com, I face players who are into gambits. Now as a matter of (cheap) fact, I rarely play positionally and more materially, so I tend to take the extra material in the opening in exchange for development. Sometimes it works, most of the time though, the development advantage easily overcomes my material plus and I get a quick, crushing defeat within 20 moves. These are some of the common gambits I face. I want to learn how (if possible) to keep the material plus AND cope up for my lack of development.
DANISH GAMBIT
Is this the right way to counter the Danish Gambit? Usually white's dark bishop plays a pivotal role in the attack, so if I can block it up with a check, I would be able to go Nf6 and go for castling in the next move. If I play this, can I keep my -2 material advantage and slow down white's assault?
What do the seniors advise in this situation?
KING's GAMBIT
What should be my (black's) top priority here? Getting a queenside castling asap or trying and launching a kingside attack on the opponent asap? What are the main ideas (for black) in this line?
HALLOWEEN GAMBIT
This is probably the most annoying opening of all. I've faced it only once or twice perhaps, but I still remember the anguish. Is there a way to keep both of my knights forward on the board and not having to return my knight back to it's starting position?
LATVIAN GAMBIT
The only question here is: WHICH DAMNED PAWN SHOULD I TAKE???