Is there one type of face as a human vampire? Bat-like nose, right?

You will retain every feature of your old face, save for glowing red or yellow eyes, a red line that runs from the bottom of the nose to the lips, bags under the eyes, paler skin, and fangs.

You will not receive the bat noses or the rougher complexions.

What if I get infected by vampirism before I meet the vampire boss in Dawnguard?

Same.