First of all, Hi Isotop
I was very intrigued about your questions, and like spy up here, initially I've just use the "common sense" to give an explanation. Anyway, after re-reading the book, i would like to show my ideas on this issue, hope to be helpful:
I try to respond to your n.2 question first, just to clarify the other clarification
"Units are a group of individuals (models) who stick together for mutual benefit." This is what the rulebook says to introduce the unit. as you can see there is two keywords: unit and models. We have a unit only when ALL the models, of the same unit, are at least 2" to another model of the same unit. in this case we have a unit in formation.
When happend, involuntarily, that one, or more, model of an unit are pushed away more than 2" from the other model of that unit, the unit is broken. If, for example, one model of my unit of 3 Cromlech Guard is pushed away from the other more than 2", the unit is broken. In this case my 2 model still near each other is consider "models in formation" and the single one is "out of formation". if we ipotize that my unit was formed by 4 models and two models of that unit was pushed away like in the up above example, i will find my unit BROKEN in two groups of two model, each group with the model close enough to be in formation singly. As i say, the unit is broke in anycase, but the models are anyway in formation cause the 2" with another model of the same unit. This is the case of the example on pag.61 of the rulebook, where there is a group of 2 Hoplites, in formation. the single one, out of formation, in the middle, and the three models on the right, also them in formation with each other.
This is the difference of unit formation and models in formation: there is no unit formation until all the models of the unit are in formation with each other.
I think that this wall of text explain also your initial understanding on chain up the models, and your first question indeed
For your last question i think that if a model is the last of an entire unit, he is considered the unit anyway, just because he is the last man of that unit and, as rulebook says about the Slay movement, also if there is a single model left of an unit, he cannot anyway perform this action, thing that only the single models, like Warlord or characters can do.
As always i apologize for my bad English and i hope to be helpful. for any other question I'll be glad to try to help