Learn Hardcore Portuguese (Brazil): É importante que o aluguel seja pago hoje. - It is important that the rent be paid today.

Because after É importante que..., Portuguese normally uses the subjunctive to express necessity, importance, recommendation, or doubt about an action.
So you get é importante que + (verb in subjunctive) → seja (present subjunctive of ser), not é (indicative).

What tense/mood is seja pago exactly?

It’s the present subjunctive (seja) + past participle (pago). Together they form a passive voice structure in the subjunctive:
ser (subjunctive) + participle = to be + past participle (but in a “required/important that…” context).

Is this the passive voice? If so, what is the active version?

Yes. o aluguel seja pago is a passive idea: the rent (payment) is the thing receiving the action.
An active version could be:

É importante que você pague o aluguel hoje. (It’s important that you pay the rent today.)
É importante pagar o aluguel hoje. (It’s important to pay the rent today.) — more general/less explicit about who pays.

Why does it say o aluguel (with o) instead of just aluguel?

O is the definite article (the), and here it points to a specific rent payment that both speaker and listener know about (e.g., this month’s rent).
Without the article, aluguel can sound more general or more like “rent” as a concept, depending on context:

É importante que o aluguel seja pago hoje. (that specific rent payment)
É importante que aluguel seja pago hoje. (possible, but less natural in many contexts; sounds more generic or “headline-like”)

Why is it pago and not paga?

Because pago agrees with o aluguel, which is masculine singular.
In passive structures, the participle behaves like an adjective and matches the noun:

o aluguel → pago
a conta → paga
os aluguéis → pagos
as contas → pagas

Does aluguel mean the place you rent, or the rent payment?

In this sentence it means the rent payment (the money due). That’s the most common meaning in contexts like “paid today.”
If you mean the rental property/apartment, Brazilians would more likely specify it (e.g., o apartamento, o imóvel) rather than rely on aluguel alone.

Is que mandatory here?

With this structure, yes: é importante que + subjunctive is the standard pattern.
If you want to avoid que, you typically switch to an infinitive construction:

É importante pagar o aluguel hoje. (no que, no subjunctive)

Could I also say É importante que o aluguel esteja pago hoje? What’s the difference?

You can, but it changes the focus:

seja pago hoje = important that the payment happens today (the action of paying).
esteja pago hoje = important that it ends up in the state of being paid by today (emphasis on the result/status).

Both can work, but seja pago hoje is very straightforward for “must be paid today.”

Where can hoje go in the sentence?

Hoje is flexible, but placement affects emphasis:

É importante que o aluguel seja pago hoje. (neutral/common)
É importante que hoje o aluguel seja pago. (emphasizes today; more formal/marked)
Hoje é importante que o aluguel seja pago. (today, it’s important… usually needs a context contrast)

The original placement is the most natural in everyday Brazilian Portuguese.