New alternator. maybe battery will come good - don't hold your breath. Chean all battery terminals, cables and earth points. Check all other earth points and plugs for clean and tight. That should make most of your problems go away. Hope you both enjoy your E38 as much as I enjoy mine.
Good - Fast - Cheap: Pick any two.
E23 735i; E32 735iL (X 2 - 1 Alpine White and 1 Glacier Blue); E34 535i; E38 735iL; R50 Cooper; R55 Cooper Clubman.
E21 318i; E30 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i