A lot of times, those are videos made by players that are much more powerful, but they will remove a bunch of their power items to artificially lower their power. So, they might only have the power of a 40k player, but the defense of 300k player. More often it is the other way around. They have inflated damage for their "power". Once you get around Ninja Exam 140, you won't be able to just brute force you way through most of those reward levels.

As for the other team being faster than you, you will find that will be the case for almost all of the multiple of 10 levels. They were given artificially high init, so they should always go first, often times more than 1 ninja on that team will be able to go before you, last big level I passed their entire team of 9 ninjas went first.