A couple quick comments before I do full analyses:
Game 1: Yes, luck absolutely determined this game. I think I played really well, but... Fabian didn't get the chance; I would have probably played very nearly identically to him. On the other hand, I don't think the 2-0 provinces made as much difference as you guys are implying, but... that will be in the later commentary.
Game 2: OK, here's the big one. Bureaucrat should really stomp spice merchant. As for getting $7 3 times after turn 18 - I don't think that's a sign you got unlucky, I think it's a sign you got lucky! Let's look at your deck at that point:
Fabian: 32 points : 3 Province, 1 Gold, 3 Duchy, 2 Caravan, 1 Spice Merchant, 1 Great Hall, 4 Silver, 4 Estate, 3 Copper
So to get $8, you need either all 4 silvers, the gold and 3 silvers, the gold, 2 silvers and a copper, a gold a silver, and all 3 coppers, or 3/4 silvers and 2/3 coppers. All in all, a deck of that size... it's unlikely. On top of which, the first 2 $7s you used to buy the last 2 duchies. If either of those weren't duchies, I get the last duchy and only need 1 of the provinces anyway...
Game 4: Yes, second remodel is better as something else. I got rather unlucky to get remodel-copper-copper-estate-estate, which might have just doomed me there, but Fabian also outplayed me.
Game 5: Well, game 1 I think I had a clearly better strategy, but still wouldn't expect to win like all the time - he's got chances. Here though, was the real clear outplay, which I don't feel like I can take credit for so much 'cause I just copied the strategy I'd read on these forums! Anyway, with the strategies, I should win roughly 100% of the time, but even if he also goes for 'the golden deck', I'm going to win like, 70 % of the time or something with 1st-turn. And I was pretty sure that province is the way to go there over colony in terms of efficiency, like in a mirror match, BUT, if he's to have any chance of beating me there, it's better to go for the colonies for me, while not in the mirror. I think.