Learn Portuguese (Portugal): Não fume aqui, é proibido.

Fume is the formal (você) command form of fumar (to smoke). To form negative commands, Portuguese uses the present subjunctive. For regular -ar verbs, this means swapping the usual -a ending for an -e.

How would I change this sentence to tell a close friend not to smoke?

You would say "Não fumes aqui...". For informal (tu) negative commands, you also use the subjunctive form, which adds -es to -ar verbs. Notice that this is different from the positive informal command, which would just be fuma.

Why do we use é (from ser) instead of está (from estar) for "it is"?

We use é because rules, laws, and general truths are treated as permanent facts in Portuguese. Estar is generally reserved for temporary states or conditions, so it doesn't fit for a standing rule.

Will proibido ever change to proibida if a woman is speaking?

No, it stays proibido. When an adjective describes a general action or idea (like the act of smoking) rather than a specific noun, it always takes the default masculine singular form, regardless of who is speaking.