Learn Hardcore Russian: Я готовлюсь к уроку, смотрю расписание и проверяю пароль от компьютера. - I prepare for the lesson, check the schedule, and verify the computer password.

The verb готовиться (“to prepare oneself”) always takes к + dative to show what you’re preparing for. Here урок (lesson) becomes dative singular уроку, so готовлюсь к уроку means “I’m preparing for the lesson.”

Why is готовлюсь reflexive (ending in -сь)?

The suffix -ся marks the reflexive form of готовиться (“to prepare oneself”). Without -ся you’d have готовить (“to prepare [something or someone else]”). Reflexive verbs often indicate the action is directed back at the subject.

Why do we say смотрю расписание without any preposition, and why doesn’t расписание change its ending?

Смотреть is a transitive verb that takes a direct object in the accusative case without a preposition. Because расписание is a neuter, inanimate noun, its accusative form is identical to the nominative. Thus it stays расписание.

Why is it пароль от компьютера instead of something like пароль на компьютере or пароль для компьютера?

To express “the password for/access to something,” Russian typically uses пароль от + genitive (the password that belongs to or comes from the device).

на компьютере would mean “on the computer” (location),
для компьютера is grammatically possible (“intended for the computer”) but less idiomatic when talking about your login password.

All three verbs (готовлюсь, смотрю, проверяю) are imperfective. Why not use perfective forms?

Imperfective verbs describe ongoing, habitual, or repeated actions. Here the speaker lists routine tasks they are doing (or do regularly). To emphasize that each task was or will be completed as a whole, you would switch to perfective:
– приготовился к уроку, посмотрел расписание, проверил пароль от компьютера.

Why is there a comma after уроку but not before и in the series of verbs?

In Russian, homogeneous members (here, the verbs) are separated by commas. When two members are joined by a single coordinating conjunction и, you do not place a comma before и. Hence:
“…к уроку, смотрю расписание и проверяю пароль…”

Can you omit the subject я and simply say Готовлюсь к уроку, смотрю расписание…?

Yes. Russian frequently drops the pronoun я when the verb ending clearly shows 1st person singular. Including я adds emphasis or clarity but is not mandatory.

Could you use perfective forms for смотрю and проверяю (for example, посмотрю расписание, проверю пароль) in this sentence?

You could, but then you’d imply you will carry out and complete those actions (often in the future) rather than simply listing what you’re doing. Using perfective shifts the nuance to single completed actions rather than ongoing ones.