En la pasinta semajno mi ricevis nek retpoŝton nek mesaĝon de mia amikino.

It means neither ... nor ....

So:

mi ricevis nek retpoŝton nek mesaĝon
= I received neither an email nor a message

This is the normal way in Esperanto to join two negative alternatives. Both things are excluded.

Because nek ... nek ... already makes the idea negative.

So Esperanto can say:

Mi ricevis nek retpoŝton nek mesaĝon.

That already means I received neither an email nor a message. You do not need an extra ne.

They are the direct objects of ricevis.

The verb ricevi means to receive, so the things received are the objects:

• retpoŝton = an email
• mesaĝon = a message

In Esperanto, direct objects take the accusative ending -n.

So:

• mi ricevis retpoŝton = I received an email
• mi ricevis mesaĝon = I received a message

With nek ... nek, both objects still need -n.

Ricevis is the past tense of ricevi.

• ricevi = to receive
• ricevas = receive / am receiving
• ricevis = received
• ricevos = will receive

So mi ricevis means I received.

Pasinta means past or last here.

It comes from the verb pasi, meaning to pass.
So la pasinta semajno literally means the passed week or more naturally the past week / last week.

Pasinta is an adjective, so it ends in -a because it describes semajno.

The article la makes it definite: it refers to a specific week, the one that has just passed or the relevant past week.

So:

• la pasinta semajno = the past week / last week

Without la, the phrase would usually sound less specific.

Both can refer to last week, but they are not always felt in exactly the same way.

• pasintsemajne is a compact adverb meaning last week
• en la pasinta semajno is a fuller phrase meaning in the past week or during the last week

Depending on context, en la pasinta semajno can sound a bit like within the last week, while pasintsemajne often simply means last week.

En often means in, and here it introduces a time period: in the past week.

So:

En la pasinta semajno = In the past week

Learners may also see dum la pasinta semajno, which means during the past week. In many contexts the two are close in meaning, though dum emphasizes the duration a bit more.

Here de means from.

So:

• retpoŝto de mia amikino = an email from my female friend
• mesaĝo de mia amikino = a message from my female friend

In Esperanto, de can mean of or from, depending on context. With messages, letters, emails, and similar things, it often marks the sender.

Because amikino specifically means female friend.

• amiko = friend / male friend
• amikino = female friend

So mia amikino means my female friend.

If the meaning were romantic girlfriend, Esperanto more clearly uses koramikino.

Yes. In this sentence, it naturally applies to both.

So the meaning is:

I received neither an email from my female friend nor a message from my female friend.

Esperanto often avoids repeating the same phrase when it clearly belongs to both coordinated words.

Because the sentence is talking about not receiving even one of either thing.

So:

• nek retpoŝton nek mesaĝon = neither an email nor a message

Using the singular is very natural here. It suggests not one email and not one message.

You could use plurals in a different sentence if you wanted to emphasize multiple items:

Mi ricevis nek retpoŝtojn nek mesaĝojn.
= I received neither emails nor messages.

Retpoŝto means email.

It is built from:

• reto = network / internet
• poŝto = mail / post

So retpoŝto is literally something like internet mail.

Not necessarily. Mesaĝo is a general word meaning message.

It could mean:

• a text message
• a chat message
• a written message
• a general message of some kind

If you want to be more specific, Esperanto can use words like tekstmesaĝo for text message.

Because Esperanto word order is flexible, and the speaker is putting the time expression first.

Starting with En la pasinta semajno highlights the time frame:

En la pasinta semajno mi ricevis ...

A different order is also possible:

Mi ricevis nek retpoŝton nek mesaĝon de mia amikino en la pasinta semajno.

But the original version sounds natural and gives the time setting right away.

Yes, that is a very natural English rendering.

A few small nuances are possible depending on context:

• last week
• in the past week
• during the past week
• over the last week

And amikino specifically adds that the friend is female.