Learn Hardcore Esperanto: Tamen mia patrino jam aĉetis biletojn kaj eniros kun ni en la muzeon morgaŭ. - However my mother has already bought tickets and will enter the museum with us tomorrow.

So biletojn = tickets as the direct object of aĉetis (bought). You must use -n on a direct object; when it’s plural, the -j comes before -n: -jn.

Why does muzeon also have -n after the preposition en? I thought prepositions don’t need accusative.

In Esperanto, most prepositions normally take the nominative (no -n) form.
However, with some prepositions (especially en, sur, sub, etc.), you can optionally add -n to show movement towards a place rather than simple location.

en la muzeo = in the museum (location, where?)
en la muzeon = into the museum (movement to where?)

Here we have eniros kun ni en la muzeon = (she) will enter / go into the museum with us, so the -n on muzeon marks direction: going into the museum, not just being in it.

If eniros already has en inside it, why do we also have the separate en before la muzeon? Isn’t that redundant?

The verb eniri is made from:

en (in, into)
iri (to go)

So eniri ≈ to go in / to enter.

You still need a preposition to show where you are entering:

eniri la muzeon (without extra en) = to enter the museum
eniri en la muzeon = to enter into the museum

Both patterns exist. Many speakers are happy with eniri la muzeon (no second en), but eniri en la muzeon is also very common and feels natural, a bit like English “go into the museum” rather than just “enter the museum”.

Your sentence uses eniros … en la muzeon, which is fine and idiomatic.

Could I replace eniros with iros en and say … kaj iros en la muzeon morgaŭ?

Yes, that is grammatically correct:

… mia patrino jam aĉetis biletojn kaj iros en la muzeon morgaŭ.

Difference in nuance:

eniri = to go in / enter (focus on the action of going inside)
iri en = to go in (literally “to go in(to)”)

In practice, eniros en la muzeon and iros en la muzeon both mean “(she) will go into the museum”.
Eniri is just a more compact, lexicalized verb.

Why is it kun ni and not kun nin?

In Esperanto, prepositions (like kun, en, sur, al, etc.) normally take the nominative form (no -n), even for pronouns.

So:

kun mi, kun vi, kun li, kun ŝi, kun ni, kun ili

You only use -n with:

direct objects (of a verb), or
to show direction with some prepositions.

Here, ni is not a direct object of a verb; it’s just the object of the preposition kun (with).
So kun ni is correct; kun nin is wrong in standard Esperanto.

What is the difference between jam aĉetis and English “has already bought” or “already bought”? Does Esperanto have a special perfect tense?

Esperanto has only three simple tenses:

-as = present
-is = past
-os = future

There is no special “present perfect” tense like English “has bought”.

To express the “already” idea, Esperanto simply combines:

past tense (aĉetis = bought)
adverb jam (= already)

So jam aĉetis can correspond to:

“has already bought”, or
“already bought”

Context decides how you translate it, but in Esperanto the form is just past + jam.

What does tamen add here? Could I leave it out?

Tamen means however / nevertheless / still / even so.

It shows contrast with some earlier idea, for example:

Maybe someone said: “Ŝi ne venos.” (She won’t come.)
Then: “Tamen mia patrino jam aĉetis biletojn …”
= “However, my mother has already bought tickets …”

If you remove tamen, the sentence becomes neutral, with no explicit contrast:

Mia patrino jam aĉetis biletojn kaj eniros kun ni en la muzeon morgaŭ.

So yes, you can leave it out grammatically, but then you lose the “contrary to what you might expect” nuance.

Can I move tamen to another place, like “Mia patrino tamen jam aĉetis biletojn”?

Yes. Esperanto word order is quite flexible, and adverbs like tamen can move around:

Tamen mia patrino jam aĉetis biletojn …
Mia patrino tamen jam aĉetis biletojn …
Mia patrino jam tamen aĉetis biletojn … (less common, but possible)

All are understandable. The most natural are usually:

Tamen, mia patrino jam aĉetis biletojn …
Mia patrino tamen jam aĉetis biletojn …

Moving tamen slightly shifts emphasis, but doesn’t change the basic meaning.

Why is it en la muzeon morgaŭ and not morgaŭ en la muzeon or en la muzeon morgaŭ? Does the position of morgaŭ matter?

All of these word orders are possible:

… eniros kun ni en la muzeon morgaŭ.
… eniros kun ni morgaŭ en la muzeon.
… morgaŭ eniros kun ni en la muzeon.

Esperanto is quite flexible with adverb placement. Typical neutral choices are:

Morgaŭ mia patrino eniros kun ni en la muzeon.
Mia patrino eniros kun ni en la muzeon morgaŭ.

Changing the position may slightly affect emphasis (what you want to highlight), but not the core meaning. There is no strict rule that morgaŭ must be at the end.

Why is it mia patrino and not something like la mia patrino or la patrino mia?

In Esperanto, possessive pronouns (mia, via, lia, ŝia, nia, ilia) behave like adjectives and normally come before the noun they modify:

mia patrino = my mother
via amiko = your friend

You generally do not add la before a possessive pronoun:

mia patrino (correct)
la mia patrino (incorrect in normal usage)

La patrino mia is understandable but sounds poetic or very marked; everyday Esperanto uses mia patrino.

Why is it eniros (future) if the sentence already has morgaŭ (tomorrow)? Could I use eniris or eniras instead?

In Esperanto, the verb ending clearly marks the time:

eniris = entered (past)
eniras = is entering / enters (present)
eniros = will enter (future)

Morgaŭ indicates time too, but you still choose the verb tense that matches:

eniros … morgaŭ = will enter tomorrow

Using eniras … morgaŭ is possible in some very specific contexts (like a scheduled event, similar to English “tomorrow she enters the museum for free”), but the normal, neutral form for future is -os.

So eniros … morgaŭ is the standard and clearest choice.

What does the -in- in patrino mean?

Esperanto builds many words from roots plus affixes.

patro = father (parent, traditionally male)
-in- = female suffix
patrino = mother (female parent)

So:

patro (father)
patrino (mother)
infano (child)
filo (son)
filino (daughter)

The -in- morpheme consistently means a female person or animal.