Yes, it's the imperative singular, so you are talking to one person informally -- the du form.
The ihr form (speaking to several people informally) would be Esst nicht!, and the Sie form (speaking formally, either to one person or to many people) would be Essen Sie nicht!
Because the vowel is short.
ß is only used after long vowels and diphthongs (Buße, in Maßen, reißen) while ss is used after short vowels (Busse, in Massen).
(This is in post-1996 spelling. Before that, the rules were a bit different and were mostly about whether the sound came at the end of a syllable, so you would have spelling changes when inflecting words such as essen but iß! or Schloß but Schlösser. Now it's more uniform: essen; iss!; Schloss; Schlösser.)