Learn Hardcore Russian: Когда счёт оплачен, можно заказать такси. - When the bill is paid, one can order a taxi.

Когда introduces a temporal subordinate clause; here it means once or when in the sense as soon as the bill is paid. It links the payment condition to the main clause.

Why is счёт in the nominative case and not accusative?

Because оплачен is a short-form past passive participle acting like an adjective and agreeing with its subject. In Russian, the subject of such participles is in the nominative, so счёт appears in the nominative singular masculine.

What part of speech is оплачен, and how is it formed?

Оплачен is the short-form past passive participle of the perfective verb оплатить (to pay). It expresses the resulting state paid and in this form agrees with счёт in gender and number.

Why is there a comma after оплачен?

A comma separates the subordinate temporal clause (Когда счёт оплачен) from the main clause (можно заказать такси). In Russian, if a subordinate clause introduced by когда comes first, it is typically followed by a comma.

What does можно mean here, and why is there no explicit subject?

Можно is an impersonal modal word meaning it is possible, one may, or you can. Impersonal constructions in Russian do not show a specific subject; the allowed action applies generally.

Why is заказать такси in the infinitive form?

With the impersonal modal можно, the main verb must be in the infinitive. Here заказать (to order) expresses the permitted action, and такси is its direct object in the accusative.

Could we rephrase the sentence using a different tense or aspect for the payment clause?

Yes. For example:

Когда счёт будет оплачен, можно заказать такси. using the future tense of быть plus the participle.
После того как оплатите счёт, можно заказать такси. using a full subordinate clause with a perfective verb.
The original version with the short participle is more concise and emphasizes the completed state.