No period there. 

Do it as you describe here.

The comma is optional. You don't need it. The quote marks are optional too, in this case, but I'd use them. 

It's pre-Civil War.

Yes, I'd hyphenate it. It could initially be read differently without the hyphen, as if the benefits or the chickens are freeing a range. 

I'd make it as you have it:  An at-will associate; the company's policy of employment at will.

I'd use the hyphen.

We use it in those cases.

We prefer the week ending, though the week ended sometimes sneaks in.  I'd hyphenate year-on-year.

There's no absolutely "proper" way. As we say in the introduction to the hyphen entry:

Use of the hyphen is far from standardized. It is optional in most cases, a matter of taste, judgment and style sense. But the fewer hyphens the better; use them only when not using them causes confusion (loose-knit group, but tax code changes). Think of hyphens as an aid to readers’ comprehension. If a hyphen makes the meaning clearer, use it. If it just adds clutter and distraction to the sentence, don’t use it.

I'd say that as a noun phrase, fixed income relative value is fine without the hyphens. It might also be fine with no hyphens as a modifier. But since there are a lot of words there, you're better off hyphenating as a modifier  the fixed-income relative-value strategy.

Again, though, others may do it differently and that doesn't make them wrong, in this case.

Either is fine in common usage. If you're writing for persnickety readers, you might opt for the second option. 

It's not a term we would use, with or without the hyphens.

Do it as you have it.

A dash or a colon. Note, what you have there is a hyphen.

Blank blank is always where you need us most – close to the place your family calls home. 
Blank blank is always where you need us most: close to the place your family calls home. 

I'd use the hyphen for clarity. (The hyphen rules are the same as always, with a few exceptions. We just added more explanation and examples).

It's from. Also, AP style uses a hyphen for ranges: June 9-12.

For composition titles, yes. Here is the entry. These guidelines apply to titles of books, movies, plays, poems, albums, songs, operas, radio and television programs, lectures, speeches, and works of art.

If you're talking about the headline for a news or feature story, AP style is to capitalize only the first word and proper nouns.

Those words should be lowercase when standing alone.

Two words, as you have written it.

We use dataset.

I'd go with the numeral in this case: 3-free, 8-free.

Not in AP style. State and local governments tend to follow their own style and use the capital letter there. But in AP style, we don't.

I'd recommend hyphenated in that use, just for absolute clarity. Without the context of a full sentence, it could be a little confusing without the hyphen. At least, it could cause the reader to pause for a split second to think about it. Is there a Life Well? Is it like the fountain of youth? Like that.

It would be reasonable to do that in such a situation, if there's a possibility for confusion. As with everything, style is flexible; it can and should be tweaked to meet the needs of individual situations. This particular situation doesn't come up all that often, so no one has ever seen a need to spell it out as a one-off exception in the general guidelines. 

Best question all day! Or at least, best use of squirmy animals and I needed that right now.

Lowercase buyer's guide on second reference.

I'm so disappointed that cutegerbils.com doesn't actually exist. As an aside: Chuckanut.