Did other Dave sprite himself to gain sprite knowledge or to keep the number of Daves in the Alpha-timeline to a minimum? Can Dave take other people to different timelines? What do you think would've happened if other Dave hadn't spirited himself?

He probably did it to help Alpha!Dave.   No, he can’t take people to other timelines.

If Dave hadn’t jumped into the sprite he would have died and Alpha Dave would have been stuck with Calsprite.