The correct door height needs to be proportional to the facade. This house is in an area with a fairly low overall building height restriction so the doors are only 7 ft tall and with the transoms it's about nine feet total. In a house that can be taller such as the original manor houses in France, the doors would have been much taller.

Do you remember the name of the slate color(s)?

It's a blue-grey slate. Sorry, I don't know the name it went by.