Mi tiras la seĝon al mi, sed mia amikino ŝovas la tablon for de la pordo.

The ending -n marks the direct object in Esperanto.

• Mi tiras la seĝon = I pull the chair
• Mia amikino ŝovas la tablon = My female friend pushes the table

So la seĝon and la tablon are the things being acted on.

By contrast, la pordo does not take -n here because it comes after the preposition de in for de la pordo.

Because al mi means toward me / to me, not me as a direct object.

• Mi tiras la seĝon al mi = I pull the chair toward me
• Mi tiras min would mean I pull myself

So al shows the direction of the movement.

They describe opposite kinds of movement:

• tiri = to pull
• ŝovi = to push / shove / slide

So in the sentence:

• Mi tiras la seĝon al mi = I pull the chair toward me.
• Mia amikino ŝovas la tablon for de la pordo = My friend pushes the table away from the door.

for means away, and de means from.

Together, for de gives the idea of movement away from something:

• ŝovas la tablon for de la pordo = pushes the table away from the door

If you used only de, the idea of active movement away would be less clear in this context. for adds the important sense of awayness.

In Esperanto, a possessive adjective like mia, via, lia, etc. usually already makes the noun definite.

So:

• mia amikino = my friend

You normally do not add la before it.

Using la mia amikino is possible only in special cases, such as strong contrast or a literary style, but it is not the normal everyday form.

The suffix -in- marks female.

• amiko = friend
• amikino = female friend

So mia amikino specifically means my female friend.

That is the normal word order in Esperanto, just like in English:

• mia amikino = my friend
• la tablo = the table

Esperanto is fairly flexible, but putting the possessive before the noun is the standard, neutral way.

Yes, Esperanto word order is more flexible than English because endings and prepositions show each word’s role.

For example, these are still understandable:

• La seĝon mi tiras al mi.
• For de la pordo mia amikino ŝovas la tablon.

But the original order is the most neutral and easiest for learners:

• Mi tiras la seĝon al mi, sed mia amikino ŝovas la tablon for de la pordo.

So yes, word order can change, but the usual subject–verb–object order is best unless you want emphasis.

The ending -as is the Esperanto present tense ending.

• tiras = pulls / am pulling / pull
• ŝovas = pushes / is pushing / push

Esperanto uses the same present-tense ending for all persons:

• mi tiras
• vi tiras
• ŝi tiras
• ili tiras

So the verb does not change the way English verbs do.

Two letters here are especially important:

• ŝ sounds like sh in ship
• ĝ sounds like j in judge

So:

• ŝovas starts with a sh sound
• seĝo has the j sound in the middle

Stress in Esperanto is always on the second-to-last syllable:

• TI-ras
• SE-ĝon
• ŝO-vas
• a-mi-KI-no
• POR-do

That stress rule is very regular, which makes pronunciation easier once you learn it.