Learn Hardcore Russian: Учитель начинает урок.

урок is a noun in the accusative case, serving as the direct object of the verb. Since урок is inanimate, its accusative form is identical to its nominative form.

Why isn’t there any article before Учитель or урок?

Russian does not use articles (like “the” or “a/an” in English). Context tells you whether you mean something definite or indefinite.

What tense and aspect is начинает?

начинает is present tense, third-person singular of the imperfective verb начинать (“to begin” or “to start”). Imperfective verbs describe ongoing, repeated, or habitual actions.

Could you show the full present-tense conjugation of начинать?

Sure:
я начинаю – I begin
ты начинаешь – you (sing.) begin
он/она начинает – he/she begins
мы начинаем – we begin
вы начинаете – you (pl. or formal) begin
они начинают – they begin

Where is the stress in начинает, and how is it pronounced?

Stress falls on the third syllable: начи́нает. Pronunciation roughly: nah-chee-NAH-yet.

Is word order fixed? Could you say Урок начинает учитель instead?

Word order in Russian is more flexible than in English. Урок начинает учитель is grammatically correct but emphasizes учитель less (it can feel like “It’s the teacher who starts the lesson,” perhaps contrasting with someone else).

Why is there no preposition before урок like in “begin the lesson” in English?

In Russian you directly take an object in the accusative case after начинать. You don’t need a preposition for “beginning” something; the verb itself governs the direct object.

What would change if the teacher started multiple lessons, i.e. plural?

Subject and object stay nominative and accusative, but урок becomes уроки (nominative/accusative plural) and начинает becomes начинают (3rd person plural):
Учитель начинают уроки. (Literally “The teacher(s) begin lessons.”)