Yes puppies are born with the coat theyre destine to have
this is a great page that explains the coats in depth
http://yorkiepassion.com/coatcolorchanges.htm
the above is a great article written by Joan Gordon
as far as the eye flash...
all puppies will flash blue as the mature they will flash various shades green, golden, greenblue, amber or red.
Green or varies shades of green is usually a silk coat (but not always)
a modified coat will also throw a green depending what kind of modified.
A black modified that will more than likely remain black as an adult will usually throw a red or amber eye.
hope this helps
