Last year the SW parade was at 12:40pm, it will likely be at that same time this year but no official word yet
No, they give out the fp's all the way to the right, there are large gates you enter thru those, the CM will give out the fp, wristband and scan your tickets, then you enter thru backstage near the restrooms and the stroller rental. That's what happened last year.
As to the JTA question, there are plenty of people getting kids sined up for this and it goes by very quickly, like I've said before it's booked up 25 min. after park opening.