I'm not totally familiar with the offside rules but as far as I can tell, they apply when the ball is received and on none of those occasions could I see a player in the offside section. The ruling in the game should have been a goal.
Totally out of my realm, though: someone more familiar with football should chime in.

No, the offside rule applies from when the ball is played to the guy ruled offside (the second it leaves his team mates foot/chest/head).