The answer to your first question is no. There are non-ribbon boundary links whose components are unknotted! Indeed the Bing double of a knot is a boundary link with unknotted components, but it has recently been proven by several authors that the Bing double of the figure-8 knot is not slice (hence not ribbon.) See for example [this paper.][1]

Edit: The Bing double of the trefoil is also not slice, which is a less subtle calculation using the signature.


  [1]: http://arxiv.org/abs/0709.2968