"I am not eating."
Translation:Ich esse nicht.
Ja, ist nicht korrekt. Korrekt ist: Ich esse nicht. Siehe hier: http://www2.germanistik.uni-freiburg.de/dafphil/internetprojekte/projekte5/deutschlandreise/hhg.html The inflected verb is always in second position.
Is the word Ich necessary in this sentence? Esse only conjugates to first person singular so would the subject 'ich' be already implied?
No, because in German (as with many other languages such as Spanish, Italian French etc) the present tense covers both things that you do: I eat and things that are continuously happening: I am eating (or in this case, not eating)