I think there is not a rule. "Uscire con amici" is more vague than "Uscire con gli amici", which is more vague than "Uscire con i miei amici", which is different from "Uscire con miei amici".
"Uscire con amici" gives the idea of the fact per se, without specifying which friends (mine? your?). The same is "Uscire con gli amici", but the determinative article restricts just a little the concept, implying that those friends are the abitual ones.
"Uscire con i miei amici" is the more precise one: it specifies clearly "my" (abitual) friends.
"Uscire con miei amici" (or "Uscire con certi miei amici") is legitimate but strange and probably uncommon, to speak more generally, intentionally leaving out the article and giving a sense of vagueness.
And then yes, "Il vestito è grigio" is perfectly valid and the context must be present to understand which dress the phrase refers to.
An easy example comes to my mind where Italian is quite different from English: "I feel pain in my knee" is normally said in Italian as "Ho male al ginocchio", without using my/mio. In such cases (talking about the body) the context is mostly available, so italians tend to omit the possessive: "Use your hand" translates to "Usa la mano" or "Usa una mano", where "Usa la tua mano" can be said to reinforce that you should use your own hand, not the one of someone else...