Is yeast an enzyme?

No, yeast is a eukaryotic organism (bacteria are prokaryotic) and yeast is used as a rising agent in making bread, but also as a model organism in biological studies.

 

yeast contains enzymes, eg alcohol dehydrogenase

 

yeast is regarded as Fungi

 

No, not all yeasts can grow as a fungus. Some yeasts grow by budding (bakers yeast) others are dimorphic and can also grow as filliaments (candida).

 

Eduard Buchner, 1860–1917, German chemist, who taught at Berlin, Breslau, and, from 1911, at Würzburg. He discovered (1896) that alcoholic fermentation of sugars is caused by yeast enzymes and not by the yeast cells themselves. Zymase, part of the enzyme system causing fermentation, was discovered by him in 1903. For this work he received the 1907 Nobel Prize in Chemistry. Source - The Columbia Encyclopedia, Sixth Edition. 2001. (online edition)

 

I think I know what you meant. Yeasts don't always grow like many fungi, as filamentous mycelium. However all yeasts are fungi.
ref: http://ithacasciencezone.com/biozone/lessons/02class/taxonomy/Default.htm