Post la laboro mi iras al la banko, ĉar mi devas kontroli mian konton.

Post means after. The phrase post la laboro literally means after the work, but in natural English we would often say simply after work.

Esperanto often uses la where English would not. Here la laboro usually means the work/day’s work already understood from context, so post la laboro is a very natural way to say after work.

Also, laboro stays without -n here because it is the object of the preposition post, not a direct object.

Not necessarily. Mi iras al la banko literally means I go to the bank or I am going to the bank.

In Esperanto, just like in English, the present tense can be used for:

• a habitual action: After work I go to the bank
• a planned or expected action: After work I’m going to the bank

If the speaker wanted to emphasize the future more clearly, they could say mi iros al la banko. But mi iras is completely normal here.

Al means to or toward. Since the speaker is going to the bank, Esperanto uses al:

• iri al la banko = to go to the bank

The noun banko does not take -n here, because it is not the direct object of the verb. It is part of a prepositional phrase introduced by al.

La means the. In this sentence, la banko means the bank as a specific place the speaker has in mind.

Esperanto uses la much like English does for specific things already known or understood from context. So:

• al banko would sound incomplete or unnatural in most normal situations
• al la banko is the expected form for to the bank

Ĉar means because. It introduces the reason for the first part of the sentence:

• Mi iras al la banko, ĉar... = I’m going to the bank because...

After ĉar, Esperanto keeps normal clause structure. You do not need to change word order in a special way. So:

• ĉar mi devas kontroli mian konton = because I have to check my account

This is a very common Esperanto pattern:

• devas = must / have to
• kontroli = to check

The first verb, devas, is the conjugated verb.
The second verb, kontroli, stays in the infinitive form ending in -i.

So:

• mi devas kontroli = I have to check

This works like:

• mi volas iri = I want to go
• mi povas veni = I can come

Because konton is the direct object of kontroli, and adjectives must agree with the nouns they describe.

Here:

• konto = account
• mian konton = my account

Since konton is a direct object, it gets the accusative ending -n.
And because mian describes konton, it also gets -n to match.

Compare:

• mia konto = my account
• mi kontrolas mian konton = I check my account

This agreement rule is very important in Esperanto.

Yes. Possessive words like mia, via, lia, ŝia, nia, and so on behave like adjectives in Esperanto.

That means they agree with the noun in:

• number
• case

So you get forms like:

• mia konto = my account
• miaj kontoj = my accounts
• mian konton = my account as a direct object
• miajn kontojn = my accounts as direct objects

Yes. Esperanto word order is fairly flexible because endings show the grammar clearly.

The sentence as given is very natural and neutral:

• Post la laboro mi iras al la banko, ĉar mi devas kontroli mian konton.

But other orders are also possible, for example:

• Mi iras al la banko post la laboro, ĉar mi devas kontroli mian konton.

That said, the original version sounds smooth because it starts with the time expression post la laboro.

Because ĉar mi devas kontroli mian konton is a subordinate clause giving the reason. In Esperanto, it is very common to separate such clauses with a comma.

So the comma helps show the structure clearly:

• main clause: Post la laboro mi iras al la banko
• reason clause: ĉar mi devas kontroli mian konton

You will often see commas before conjunctions like ĉar in normal Esperanto writing.