You wrote:
“The question is whether there is any Biblical basis for the notion of dead people praying for each other.”
Your premise is completely false. No orthodox Christian believes the saints in heaven are dead. Perhaps heretics believe that, but we don’t.
As St. Paul says, when we die, Charity alone remains. The communion of saints is a communion of love, which is never interrupted. We can pray FOR those with us, those who went before us, and those who come after us.
In general, we as Catholics are asked not to pray TO anyone who is not canonized, since we do not know whether they are in heaven or in some other place.
But saints in heaven, recognized by the Church as examples of heroic virtue and confirmed by verified miracles, are very free to pray for us. So we should not hesitate to ask them for insight, guidance, and grace from the Redeemer. He is a King after all, and fully capable of delegating tasks to those under His dominion, who are bound by holy obedience and love to His Will.
Peace on St. Joan of Arc’s feast day!!
I think you are taking the poster too literally when “dead people” is used. I read it as “people that have died” and in the context of the discussion that would make them the “saints in Heaven”.
Anyway, that is how I took it.