Hakata to Shinagawa

I know that the JR Pass can't take Nozomi on Sanyo Shinkansen. Please advise the follows:
1) Which type of Shinkansen can we take?
2) What is the earliest departure from Hakata to Shinagawa?
3) Do we need to transfer?
4) Can we get a seat assignment?
5) After we get seat assignment, can we still change the time?
6) How long it will take to arrive Shinagawa?

Look forward to hearing from you.

Thanks.