iss! is the command form or imperative.
The conjugation table just shows the indicative mood used for normal statements, not the subjunctive, conditional, or imperative moods.
Compare English: if you just look at a table that says "I am, you are, he/she/it is, we are, you are, they are", it will be "hard for you to find any reason" to use "be" in a command such as "be quiet!", but that's what English needs there because commands use the imperative mood, not the indicative.
Note that iss! is specifically the form for du. If you are addressing a command to ihr or to Sie, the forms are esst! and essen Sie!, respectively. (Those happen to be the same as the indicative forms. And note that the Sie has to be included in a command addressed to Sie, unlike a command addressed to du or ihr where no pronoun is used.)
See also the thread started by Sjodni, which already covered this. (Starting at "you wouldn't say, du iss, so why does it get used?")
It's a bit simpler, I believe. There are two conjugated verbs in this sentence, so although they're both about "du", they're about different "du"-subjects (since one subject cannot have 2 conjugated verbs refer to it). Therefore they belong to different clauses.
Again, a clause is, in simple terms, a subject+verb combo. The first clause just happens to have the subject (du) dropped. Clauses are always separated by commas. It's not very strict in English, but is very strict in Russian, for example (my native). I'm sure it's the same here.
It is the imperative (command) form, which is not the same as the normal "du" form.
Much as in English, we say "Be quiet!" even though we do not say "I am quiet but you *be not quiet." -- that verb has a separate imperative form.
See, for example, http://www.duden.de/rechtschreibung/essen , which lists in the conjungation table under "Präsens" "du isst" in the "Indikativ" column and "iss!" in the "Imperativ" column.
In general, the imperative form has no ending such as -(s)t, but the vowel may change if the "du" form does so (essen, du isst, iss!; sehen, du siehst, sieh!).
Sometimes it has an -e ending which is usually optional, e.g. http://www.duden.de/rechtschreibung/fragen which has both "frag!" and "frage!".