Can blue (lightweight) drywall compound be used for all coats?
You can use either all the way through.  I have personally used both all the way through more than a few times and have mixed.  There are generally some differences.


the lightweight end mix is thicker, meaning that the regular can actually be better for a final coat since it goes on thinner
the lightweight is easier to sand but I hardly sand... so this hardly ever helps me
I personally think the lightweight dries out faster 
lightweight does scratch and dent easier due to less density


Pros will use the regular since they can use a "less fluffy" mix that feathers easier (with little to no sanding).  But I could definitely see why a person with less experience would do the first two coats with regular and last two with lightweight.

Answers to your questions -


You are both a little right/wrong.  If I had to choose I would pick him. 
If he knows what he is doing he doesn't sand much and doesn't need lightweight.
I answered these above.  The marketing for the lightweight is for the novice DIYer that hates to spend hours sanding...