what is a good distance between each hook? also, do the number of hooks need to odd numbers?

I bought a ready made coat rack ( a board with 5 hooks) at a large box store and there is 5" inches between each hook. Hope this helps.

Refarding distance between coat hooks: if they are those old-fashioned double hooks that have a short hook for coats and a long hook above it for hats, then I would suggest a greater distance between them, in the hope that people will begin wearing hats again: men's hats are usually over 12" wide, so if everyone was wearing a fedora you'd want a good 12" – maybe 18" between coat hooks.

(ReGarding!)