Disney's queue is really long everywhere you go. Best is try to avoid weekends. Do be prepared to queue and get toys ready to distract your kids. It doesn't matter if it's evening or day. Make use of Fast Pass. But even fast passes for each rides can run out really fast. So just go to the main attraction to get the fast pass, queue for another one and then go back and redeem your fast pass.  They give you a timing on your fast pass on when your time slot to return  to that attractions.

I believe you cant pay for fastpass
Get a strategy guide to get the best of tokyo disney.