Yeah, that was an ugly one and there were a few others that looked questionable, but the defender looked like he got the ball first. But when you say "ZERO fouls in the game"... do the three fouls and two advantages in your favor not count?
As for defending, I understand any frustration with the user AI teammates lax off the ball marking. I have my User Marking slider raised for this reason when playing offline. However, you're not doing yourself any favors by immediately rushing the ball when you switch to a nearby defender or pulling guys out of your backline to chase.
I think a good deal of your frustration lies in the fact your are attempting to play FIFA12 as if it were a previous version of the game. Work on keeping your defender goal-side, don't always focus on immediately winning the ball back, and if you're not controlling the defender nearest the ball you need to mark any nearby runners.
Offense is more difficult to assess, as everyone has their own style of play and it greatly depends on your team's strengths/weaknesses. Based on that video, my suggestion would be to be more patient. It appears you don't have the team speed to counterattack or attack so directly. Try holding the ball up, not always dribbling forward, and when the pressure comes you'll be better able to change direction. It will also allow your players more time to join the attack which can give you more options and make you less predictable in your passing.