Po pracy wylogowuję się z konta i zamykam laptop.

Because po in the sense of after takes the locative case in Polish.
The noun praca changes to its locative singular form pracy.

So:

• praca = work
• po pracy = after work

You will see the same pattern in phrases like po szkole = after school and po obiedzie = after lunch.

Because the normal Polish verb is wylogowywać się or wylogować się, meaning to log out. The się is part of the verb.

So:

• loguję się = I log in
• wylogowuję się = I log out

English does not use a reflexive word here, but Polish does. Without się, the verb would sound incomplete or unnatural in this meaning.

This is a question of aspect.

• wylogowuję się is imperfective
• wyloguję się is perfective

In practice:

• wylogowuję się can describe a habit, a routine, or an action in progress
• wyloguję się usually means I will log out once, as a completed future action

So in Po pracy wylogowuję się z konta..., the speaker sounds like they are describing a usual routine after work.

Here z means from / out of, and with that meaning it takes the genitive case.

The noun is:

• konto = account
• z konta = out of the account / from the account

So wylogowuję się z konta means I log out of the account.

Be careful: z can take different cases depending on meaning. Here it is genitive, not instrumental.

Because Polish has no articles. There is no direct equivalent of English a or the.

So z konta could mean:

• out of an account
• out of the account

And zamykam laptop could mean:

• I close a laptop
• I close the laptop

Which one is meant depends on context.

Because laptop is a masculine inanimate noun, and in standard Polish its accusative singular is the same as its nominative singular.

So:

• laptop = nominative
• zamykam laptop = accusative, but the form stays laptop

Compare that with a masculine animate noun:

• kot = cat
• widzę kota = I see the cat

So zamykam laptop is grammatically normal.

Because Polish usually drops subject pronouns when they are already clear from the verb ending.

In this sentence:

• wylogowuję already means I log out
• zamykam already means I close

So ja is unnecessary unless you want emphasis or contrast, for example:

• Ja wylogowuję się z konta, a on nie = I log out of the account, but he does not

Yes. Polish word order is much more flexible than English word order.

The version you have is neutral and natural:

• Po pracy wylogowuję się z konta i zamykam laptop.

But other orders are possible if you want different emphasis, for example:

• Wylogowuję się z konta po pracy i zamykam laptop.
• Po pracy zamykam laptop i wylogowuję się z konta.

The meaning stays similar, but the focus can shift a little. Putting po pracy first is very natural because it sets the time frame right away.

Literally, zamykam laptop means I close the laptop or I shut the laptop.

If you specifically want turn off, Polish more often uses:

• wyłączam laptop
• wyłączam komputer

So zamykam laptop suggests physically closing it, or more loosely finishing with it and shutting it.

Then you would normally use perfective verbs:

Po pracy wyloguję się z konta i zamknę laptop.

That means something like After work, I will log out of the account and close the laptop.

So the contrast is:

• Po pracy wylogowuję się z konta i zamykam laptop = a routine / what I usually do
• Po pracy wyloguję się z konta i zamknę laptop = one completed future sequence