You get ahead of his driveline alot, which is why he stops; he's confused as to whether you want him to 'go' or 'stop'. An easy way to remember your proper position is to simply keep your eyes on his flank; if you are ahead or behind his flank, you are in the wrong position, and you will confuse your horse.
Another thing, when retraining, or training a horse to longe is to keep the line short, until he understands 'go' and 'stop' and 'switch directions', this way you can guide the line easier without confusing him.
As far as getting him to go, position yourself slightly to the offside of his shoulder, point your hand in the direction you want him to go, click, and with the whip or extra line if he doesn't move off, direct it at his hip.
Clinton Anderson's Downunder Horsemanship book has good tips on how to get a horse to longe.
As far as riding, he doesn't look 'off' to me, anymore...in the first vid he looked slightly off on the left front, but he doesn't seem to favor it in the second video. I'd just take it slow for a while.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."