Because supon is the direct object of preparas, and adjectives in Esperanto must agree with the nouns they describe. Since supo becomes supon, legoma also becomes legoman.
So:
Because the subject stays the same. In Esperanto, just as in English, you can mention the subject once and then connect two verbs with kaj:
ni preparas ... kaj manĝas ...
Repeating ni would also be possible, but it is unnecessary unless you want extra emphasis or clarity.
Kune is an adverb meaning together. Here it tells us how the eating happens: we eat it together.
Its position is fairly flexible. For example, all of these are possible:
The version in the sentence sounds natural and clear.
The ending -as marks the present tense in Esperanto. Depending on context, this can mean:
So the sentence could be part of a general routine or a live description. The form itself does not force only one interpretation.