When you play this variation you're generally going along the lines of the queen's gambit. At least, if you're familiar with the queen's gambit it should be comfortable to you. Generally, the c5 advance is wrong because it takes pressure off of d5.
I prefer 7 Be2. He can break your Bb5 pin by castling, you cannot do the same. Just because he pins you is no reason to do the same unless it helps your position.
Your comment about move 7 is not quite right. After 7...Qa5+ 8 Nc3 Bxf3 White should play gxf3 to hold onto the d-pawn; doubled pawns are probably better than losing a pawn. Still, you should think of these lines before you play Bb5.
8 h3 is ok but not great. Avoid moves that weaken your king's defense, in this case the square g3. I would consider 8 0-0.
10 Bxc6... I would not trade off my bishop so lightly. Two bishops plus a space advantage are usually too valuable to trade away so thoughtlessly. You could have developed a new piece to protect d4 instead, e.g. Be3.
In any case, some lucky mistakes by your opponent led to a quick checkmate. Well done. I think an important area where you can improve is bishops/knights. Which positions favor one or the other? When is it right to trade one for the other?
What was my best option other than 18. Nc3. and leading up to it? If Black played 18...NxN as I expected, what next?
Thank you for the help.