No. The concept of vampires has been around in various forms in folklore long before Dracula. In Greek mythology, there were creatures with vampiric tendencies. The Dracula story was very influential, but it was not the first. Bram Stoker just popularized the vampire concept in a more modern and widely recognized way.
No. There were earlier vampire tales. For example, the story of the 'Vampire of Croglin Grange' predates the Dracula story. Also, some ancient folklore from different cultures had elements of vampiric creatures before Bram Stoker wrote Dracula.