In theory, if the passer touched the ball twice then (say it bounced on his foot as he lifted it) then it's not allowed. But it's not possible to see that so it's a good goal.
The question is, why would anyone choose to take a free kick like that? So many things can go wrong.
Yup, it's a good one. According to the rules, "a direct free kick can be taken by lifting the ball with a foot or both feet simultaneously, the ball is in play when it is kicked and moves."