Learn Russian: Я выключаю телефон.

You would drop the subject Я and use the word можно (is it allowed / is it possible) followed by the infinitive of the verb. Because you are asking about a single completed action, you would typically use the perfective infinitive выключить, making the sentence: Можно выключить телефон?

The English translation says 'my telephone', but I do not see a word for 'my' here. Is it just implied?

Yes! In Russian, possessive pronouns like мой (my) or твой (your) are often left out when the owner is obvious from the context. Since the subject is Я (I), it is naturally assumed that you are turning off your own phone.

Why does the word телефон not change its ending since it is the direct object receiving the action?

The word телефон is actually in the accusative case here, which is the required case for direct objects. However, for masculine inanimate nouns (objects that are not alive), the accusative case form looks exactly the same as the basic dictionary form. So it stays as телефон.

What is the infinitive of выключаю and what kind of verb is it?

The infinitive is выключать (to switch off / to turn off). It is an imperfective verb, which means it describes an ongoing, habitual, or present action. Its perfective partner, used for a one-time completed result, is выключить. If you wanted to say 'You must not switch off the phone' you would use the imperfective: Нельзя выключать телефон.