Efter att hon hade gått på toaletten kom hon tillbaka och frågade efter kannan.

Efter by itself is usually followed by a noun phrase, for example efter lektionen (after the lesson).

Here, what follows is a whole clause: att hon hade gått på toaletten.
So Swedish uses efter att to mean after when introducing a full clause.

A simple way to think about it is:

• efter + noun → efter mötet
• efter att + clause → efter att hon hade gått ...

Hade gått is the past perfect (also called the pluperfect). It is formed with:

• hade
  • supine form
• here: hade gått

It shows that this action happened before another past action.

Sequence in the sentence:

1. she went to the toilet
2. she came back
3. she asked for the jug/pitcher

Using hade gått makes that earlier action very clear. If you used gick, the sentence would sound less precise about the time relationship.

Yes, på often means on, but in Swedish prepositions are often idiomatic.

Gå på toaletten is a fixed expression meaning go to the toilet / use the bathroom.

It does not mean literally walking on top of a toilet.

This is similar to how languages often use prepositions in ways that do not match English exactly.
If you are talking more literally about movement toward the room, gå till toaletten can also occur, but gå på toaletten is the very common idiomatic phrase for using the toilet.

In this expression, Swedish normally says gå på toaletten, with the definite form.

So even though English often says go to the toilet or go to the bathroom, Swedish commonly uses the form here.

Grammatically:

• en toalett = a toilet
• toaletten = the toilet

In this sentence, it is part of the set phrase gå på toaletten.

This is because Swedish is a V2 language. That means the finite verb normally comes in the second position in a main clause.

The sentence begins with the fronted clause:

Efter att hon hade gått på toaletten

After that, the main clause begins. Since the first position is already taken by that time clause, the finite verb must come next:

• Efter att ... kom hon tillbaka

So the pattern is:

1. fronted element
2. finite verb
3. subject

That is why you get kom hon, not hon kom.

Yes, you could, but in this sentence it is more natural to leave out the second hon.

Swedish often omits the repeated subject in the second part of a coordinated clause when the subject is the same:

• kom hon tillbaka och frågade efter kannan

This is smooth and natural because the same person is doing both actions.

Adding och hon frågade ... is possible, but it can sound a little more explicit or slightly heavier unless you want emphasis.

Fråga efter is an expression meaning something like:

• ask for
• ask to have
• sometimes ask where something is / ask to be given something

So frågade efter kannan means she was asking for the jug/pitcher.

This is different from some other uses of fråga:

• fråga någon = ask someone
• fråga om något = ask about something
• fråga efter något = ask for something / ask where it is / request it

So efter here is part of the verb expression, not the regular English-style meaning after.

Kannan is the definite form, meaning the jug/pitcher rather than a jug/pitcher.

That tells you it is a specific one that is already known from the context.

Forms:

• en kanna = a jug/pitcher
• kannan = the jug/pitcher

Since kanna is an en-word, the definite singular ending is -n. Because the noun already ends in -a, the result is kannan.

Tillbaka means back.

So kom tillbaka means came back / returned.

It is very common with verbs of movement:

• kom tillbaka = came back
• gå tillbaka = go back
• åka tillbaka = go back by vehicle / travel back

In this sentence, it shows that after going to the toilet, she returned before asking for the jug/pitcher.

Yes. It is very natural Swedish.

A common pattern is:

• time clause first
• then main clause with V2 word order
• then another coordinated action

So this sentence neatly presents a sequence:

• Efter att ...
• kom hon tillbaka
• och frågade ...

This is a very typical way of linking past actions in Swedish, especially in narration.