You can get a seat reservation before your pass is "activated" as long as the printed date on the JR Pass is within the date of your reservation.
For example:
You have a Japan Rail Pass voucher, you arrive on Monday the 1st, but you want to travel on Wednesday the 3rd.
You can exchange the Japan Rail Pass voucher for the actual Japan Rail Pass on Monday the 1st, with a start date listed as the 3rd (the exchange form asks you when do you wish to first activate/use the pass). They will give you the real Japan Rail Pass on the 1st, but the printed date will just say it starts on the 3rd. From then on, you are still able to make any future reservations on the 1st, even though your pass is not active yet, just as long as those future reservations are for the 3rd or later.
I don't expect Vernal Equinox to be of particular high traffic, not different from any other day.
As for you and your brother making reservations together, as long as there are seats available, and you are making reservations at the same time, I don't see any reason "why not" you can't get seats together.
Remember there is no direct Hikari Shinkansen from Tokyo to Hakata (only Nozomi's go direct), so when making reservations you will need to make two reservations, one for your first train and one for your second connecting train. You will most likely need to transfer at Shin-Osaka, if not Okayama in most cases.