Exd5 is not a mistake at all. In fact its mainline scandanavian. 1.e4 d5. 2. exd5 Qxd5 3..Nc3 Qa5
My first real try at the Scandinavian Defence

The Scandinavian is a good opening choice so long as you don't lose too much time getting your queen chased around. After 1. e4 d5 2. Nc3 black should just grab the centre with 2. ...d4 3. Nce2 e5 and enjoy having the extra space:
My 2 cents...
2)dxe5. The bishop there blocks your pawns and is poor. Thankfully for you he traded and the mess cleared up, I would have left that alone so your pieces were in your own way, playing d4 as white in response to your bishop oddity.
11) queen can drop back and prevent the pawn loss to the knight. The rook can also move up once. Look closer if you think that fork/pawn loss is not stoppable. Giving up the rook is even worse, the pawn, I can sort of understand if you did not see a rescue, but why let him eat your rook, which is valuable and well placed???? That had nothing to do with your opening, it was just a blunder.
18) letting a pin sit is usually a good way to get swindled. Break the pin here, move the queen. I think d4 would have been bad for you but white missed it. Its no good right away due to your attack potential but its there to be used at some point, maybe, and still something to be wary of.
The mate is simply white not paying attention, good for you but learn as well from your many mistakes here. His rook or simply not moving his bishop would both have saved him, just suicidal greed.
You had a won game anyway, a piece up, all things been equal I think you could have won even if he had bothered to block your queen attack.
This is the one to watch out for as black (apart from dragging the queen out early and getting in trouble with that).
Basically, the opening to me is a gambit. You let white take it and then give white the chance to defend his extra pawn. Defending it leads to poorish positions for white -- moving pieces twice in opening, odd pawn structure, etc. A skilled white player simply takes his pawn and ignores you from there, and that is usually either equal with the usual favor (first move) for white or worse for black (if you do not know opening theory enough to develop a position in this situation.
astronomer, I've actually been trying the Icelandic Gambit a bit today (glad to finally learn its name!) and I've achieved fairly decent results so far - when I get around to annotating them I'll post them. I liked your game vs mafurth - I found it instructive and entertaining.