Learn English – What does “was born in black and white” mean

It refers to the time of youth when one was naive and inexperienced, and therefore happy and optimistic - in other words, when one was "green," as in "unripe" or "not yet mature." It's a bit of a convoluted pun.

Like so many English idioms, the term was coined by Shakespeare in the 17th century (Antony and Cleopatra.)

Black dog is an oft-used phrase to mean depression.

Here's a link that attributes the phrase to Winston Churchill, but I suspect he didn't invent it. I like the way they described it though:

"Black Dog" was Churchill's name for his depression, and as is true with all metaphors, it speaks volumes. The nickname implies both familiarity and an attempt at mastery, because while that dog may sink his fangs into one's person every now and then, he's still, after all, only a dog, and he can be cajoled sometimes and locked up other times.

This paper (PDF, sorry), claims several references in the 1800's. Interestingly, the way they describe it (being ghostly and following people around) makes one wonder if it isn't ultimately related to the English folklore character Black Shuck.