Inline fuse question?

[IOWNATRUCK]

I replaced my radio the other day with a jvc aftermarket cd player, and when i was hooking up the Red wire i noticed it was worn and old, so i replaced the wires, but the original had an inline fuse, so would it be okay to run the new wire without an inline fuse?
Also, on the fuse box there was an empty spot labeled "Battery" and since the old radio didnt need a constant power wire, i hooked one up from there, is that ok? any opinions are appreciated, thanks.