I would also argue that (2)people never believe "on faith." They believe because they think they have a good reason or reasons to do so, even if that reason is not acceptable to others. A "reason" is not faith.
We may use rationalism and empiricism to reach conclusions, but it is by faith that we accept these conclusions as truth. I would say that faith is not a method of acquiring information, but rather the decision or action of accepting information as truth.
Does it require "faith" to beleive in such circumstances? I would say no: the belief is rational, although not certain. It could be that religious belief is of this nature, in the sense that there are reasons but the reasons are internal.
I agree that this is how it is in religious belief. People do not just "believe on a whim" they have their reasons.
Does it require faith to believe in such circumstances? Believing IS faith, so yes. As you said, reason alone cannot provide anything that is perfectly certain, but we know that there is a true/false answer to this question so faith is the decision to move that item in question from "uncertain" to "certainly true" or "certainly false". We use faith all the time even if we claim to not "believe" in faith, because we could not function unless we allow ourselves to be certain about some things. We know from experience, that in this particular example of a loving relationship, the relationship can be greatly hindered by a lack of "trust" or "faith" in the love of the other person.
™ Version 4.2